Journal of Combinatorial Optimization最新文献

{"title":"Submodular maximization under knapsack and partition matroid constraints","authors":"Dongkai Xu,Jianhua Yuan,Zhongzheng Tang","doi":"10.1007/s10878-026-01470-z","DOIUrl":"https://doi.org/10.1007/s10878-026-01470-z","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"22 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149020998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An FPT approximation algorithm for the partition set cover problem with penalties","authors":"Hao Zhang,Bo Hou,Gengsheng Zhang,Ke Li,Wen Liu","doi":"10.1007/s10878-026-01476-7","DOIUrl":"https://doi.org/10.1007/s10878-026-01476-7","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149021000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-set function maximization with application in viral marketing","authors":"Chensheng Ma,Hongbin G. Du,Hongmin W. Du,Zhao Zhang","doi":"10.1007/s10878-026-01475-8","DOIUrl":"https://doi.org/10.1007/s10878-026-01475-8","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149021001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximation algorithms for the minimum b-matching blocker problem on bipartite graphs","authors":"Ruiqing Sun,Weidong Li","doi":"10.1007/s10878-026-01464-x","DOIUrl":"https://doi.org/10.1007/s10878-026-01464-x","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"8 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149021003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lanzhou index of trees with perfect matching","authors":"Xuan Zhao,Ke Zhao,Fang Zhu","doi":"10.1007/s10878-026-01465-w","DOIUrl":"https://doi.org/10.1007/s10878-026-01465-w","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"83 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149021002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parallel-machine scheduling with weighted earliness-tardiness and optional job rejection","authors":"Ren-Xia Chen, Shi-Sheng Li, Cheng-Wen Jiao","doi":"10.1007/s10878-026-01462-z","DOIUrl":"https://doi.org/10.1007/s10878-026-01462-z","url":null,"abstract":"We address the problem of scheduling <italic>n</italic> jobs on <italic>m</italic> identical parallel machines with an unrestricted common due date, while permitting job rejection. The objective is to minimize the integrated cost, comprising the total weighted earliness and tardiness of accepted jobs along with the total rejection penalty. We show that when each job’s weight is equal to its processing time, the single-machine case is binary <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"script\">N</mml:mi><mml:mi mathvariant=\"script\">P</mml:mi></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathcal{N}mathcal{P}$$end{document}</tex-math></alternatives></inline-formula>-hard, whereas the parallel-machine variant is strongly <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"script\">N</mml:mi><mml:mi mathvariant=\"script\">P</mml:mi></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathcal{N}mathcal{P}$$end{document}</tex-math></alternatives></inline-formula>-hard for arbitrary <italic>m</italic> even without rejection. For fixed <italic>m</italic>, we first design two pseudo-polynomial dynamic programming algorithms, and then convert them into two fully polynomial-time approximation schemes. Their time complexities are <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:msup><mml:mi>n</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>ϵ</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:mrow></mml:msup></mml:mfrac><mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mo>log</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mtext>sum</mml:mtext></mml:msub></mml:mrow></mml:mfenced><mml:mrow><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfenced></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ Oleft( {frac{{n^{{2m + 1}} }}{{epsilon ^{{2m}} }}left( {log P_{{{text {sum}}}} } right) ^{{2m}} } right) $$end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:msup><mml:mi>n</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>ϵ</mml:mi><","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"22 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149003661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Directed star packing: Tractability, inapproximability, and approximation algorithms","authors":"Yue Sun, Zhikai Chen, Mingyang Gong, Guohui Lin, Dachuan Xu","doi":"10.1007/s10878-026-01466-9","DOIUrl":"https://doi.org/10.1007/s10878-026-01466-9","url":null,"abstract":"We consider the problem to cover the maximum number of vertices in a digraph using a collection of vertex-disjoint stars, each isomorphic to a candidate star in a given family. While the problem admits a complete dichotomy for the decision question on whether or not all vertices can be covered, the approximation algorithms and inapproximability for the maximization problem itself have remained largely unaddressed. We characterize a directed star by two non-negative integers <italic>s</italic> and <italic>t</italic> representing the numbers of out- and in-satellites, respectively, and study from the approximability perspective for six canonical star families, namely, (<italic>s</italic>, <italic>t</italic>)-, <inline-formula><alternatives><mml:math><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi>t</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(s, t^-)$$end{document}</tex-math></alternatives></inline-formula>-, <inline-formula><alternatives><mml:math><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mi>s</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(s^+, t)$$end{document}</tex-math></alternatives></inline-formula>-, <inline-formula><alternatives><mml:math><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mi>s</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi>t</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(s^-, t^-)$$end{document}</tex-math></alternatives></inline-formula>-, <inline-formula><alternatives><mml:math><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mi>s</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi>t</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(s^+, t^-)$$end{document}</tex-math></alternatives></inline-formula>-, and <inline-formula><alternatives><mml:math><mml:mrow><mml:mo stretc","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"16 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149003660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"K1,rdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$K_{1,r}$$end{document}-structure connectivity and neighbor connectivity in hierarchical networks","authors":"Liying Zhao, Shumin Zhang, Bo Zhu, Jou-Ming Chang","doi":"10.1007/s10878-026-01469-6","DOIUrl":"https://doi.org/10.1007/s10878-026-01469-6","url":null,"abstract":"Hierarchical networks offer numerous benefits, including improved performance, reliability, and scalability, enhanced security, easier module-based design and management, and greater cost-effectiveness. For a network <italic>G</italic> and a specific structure <italic>H</italic> within <italic>G</italic>, the structure connectivity <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>κ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo>;</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$kappa (G; H)$$end{document}</tex-math></alternatives></inline-formula> and the neighbor connectivity <inline-formula><alternatives><mml:math><mml:mrow><mml:msub><mml:mi>κ</mml:mi><mml:mtext>NB</mml:mtext></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$kappa _text {NB}(G)$$end{document}</tex-math></alternatives></inline-formula> are important metrics for assessing network fault tolerance. Specifically, when <italic>H</italic> is isomorphic to <inline-formula><alternatives><mml:math><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$K_{1,r}$$end{document}</tex-math></alternatives></inline-formula>, the structure connectivity is referred to as the <inline-formula><alternatives><mml:math><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$K_{1,r}$$end{document}</tex-math></alternatives></inline-formula>-structure connectivity. In this paper, we introduce a new class of hierarchical networks called hierarchical burnt pancake networks, denoted as <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>H</mml:mi><mml:mi>B</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgr","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"76 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149003659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact algorithms for solving the constrained convex combinatorial assignment problems with bounds and maximum penalty","authors":"Guojun Hu, Pengxiang Pan, Junran Lichen, Lijian Cai, Binchao Huang","doi":"10.1007/s10878-026-01472-x","DOIUrl":"https://doi.org/10.1007/s10878-026-01472-x","url":null,"abstract":"In this paper, we address the constrained convex combinatorial assignment problem with bounds and maximum penalty (the CCCA-BMP problem, for short). Concretely, given a set <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$M={g_{1},g_{2},ldots ,g_m}$$end{document}</tex-math></alternatives></inline-formula> of <italic>m</italic> machines (edge servers) with two bound functions <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>u</mml:mi><mml:mo>:</mml:mo><mml:mi>M</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:msubsup><mml:mi>Z</mml:mi><mml:mn>0</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$l,u: Mrightarrow Z^{+}_{0}$$end{document}</tex-math></alternatives></inline-formula>, satisfying the bound requirement <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>l</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>≤</mml:mo><mml:mi>u</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$l(g_{i})le u(g_{i})$$end{document}</tex-math></alternatives></inline-formula> for each machine <inline-formula><alternatives><mml:math><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>∈</mml:mo><mml:mi>M</mml:mi></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$g_{i}in M$$end{document}</tex-math></alternatives></inline-formula>, and a set <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>J</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn>1</mml:mn></mml:msu","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"8 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149086459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Total-neighbor-distinguishing coloring by sums of fractals of generalized Sierpiński graphs","authors":"Miguel Del-Rio-Palma, Carlos Arturo Rodriguez Palma, Simone Dantas","doi":"10.1007/s10878-026-01447-y","DOIUrl":"https://doi.org/10.1007/s10878-026-01447-y","url":null,"abstract":"The Total-Neighbor-Distinguishing Index by Sums of a graph <jats:italic>G</jats:italic> ( <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$textrm{TNDI}_{sum }(G)$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mtext>TNDI</mml:mtext> <mml:mo>∑</mml:mo> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> ) is the smallest positive integer for which there exists a total coloring such that the sum of the color assigned to a vertex and the colors of all its incident edges is distinct, for every pair of adjacent vertices <jats:italic>u</jats:italic> and <jats:italic>w</jats:italic> . Pilsniak and Wozniak (2015) introduced this notion and conjectured that <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$textrm{TNDI}_{sum }$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mtext>TNDI</mml:mtext> <mml:mo>∑</mml:mo> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> is less than or equal to the maximum degree plus 3. In 2011, Gravier et al. introduced the concept of generalized Sierpiński graphs, denoted <jats:italic>S</jats:italic> ( <jats:italic>n</jats:italic> , <jats:italic>G</jats:italic> ), which extends the notion of Sierpiński graphs given by Hinz et al. (2017) by replacing the complete graph in their definition with any graph <jats:italic>G</jats:italic> . In this paper, we verify that <jats:italic>S</jats:italic> ( <jats:italic>n</jats:italic> , <jats:italic>G</jats:italic> ) graphs satisfy the <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$textrm{TNDI}_{sum }$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mtext>TNDI</mml:mtext> <mml:mo>∑</mml:mo> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> Conjecture, when <jats:italic>G</jats:italic> is a bipartite graph, a path, a cycle, a star or a complete graph. Furthermore, we determine the <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$textrm{TNDI}_{sum }(S(n,G))$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mtext>TNDI</mml:mtext> <mml:mo>∑</mml:mo> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>S</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> when <jats:italic>G</jats:italic> is a complete bipartite, a path, a cycle, a star or a regular bipartite graph. Remarkably, these colorings also satisfy the corresponding conjecture for the Adjacent-Vertex-Distinguishing Total Coloring (AVDTC), and the <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$textrm{TNDI}_{sum }$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"19 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148883783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}