Discrete Applied Mathematics最新文献_第9页

The σ-irregularity of trees with maximum degree 5 最大度为5的树的σ-不规则度

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2025-11-25 DOI: 10.1016/j.dam.2025.11.045

Darko Dimitrov , Žana Kovijanić Vukićević , Goran Popivoda , Jelena Sedlar , Riste Škrekovski , Saša Vujošević

{"title":"The σ-irregularity of trees with maximum degree 5","authors":"Darko Dimitrov , Žana Kovijanić Vukićević , Goran Popivoda , Jelena Sedlar , Riste Škrekovski , Saša Vujošević","doi":"10.1016/j.dam.2025.11.045","DOIUrl":"10.1016/j.dam.2025.11.045","url":null,"abstract":"<div><div>The <span><math><mi>σ</mi></math></span>-irregularity, a variant of the well-established Albertson irregularity, is a topological invariant defined for a graph <span><math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> as <span><math><mrow><mi>σ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>u</mi><mi>v</mi><mo>∈</mo><mi>E</mi></mrow></msub><msup><mrow><mrow><mo>(</mo><mi>d</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>d</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, where <span><math><mrow><mi>d</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>d</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> denote the degrees of vertices <span><math><mi>u</mi></math></span> and <span><math><mi>v</mi></math></span>, respectively. Recent research has successfully characterized chemical trees with the maximum <span><math><mi>σ</mi></math></span>-irregularity. In this paper, we expand upon this research by establishing several structural properties of maximal trees with prescribed maximum degree <span><math><mi>Δ</mi></math></span>. Application of these properties enables us to characterize maximal trees with <span><math><mrow><mi>Δ</mi><mo>=</mo><mn>5</mn><mo>.</mo></mrow></math></span> We establish that extremal trees contain only vertices of degrees <span><math><mrow><mn>1</mn><mo>,</mo></mrow></math></span> 2 and <span><math><mi>Δ</mi></math></span>. Moreover, the number of edges with both end-vertices having the degree 2 or <span><math><mi>Δ</mi></math></span> is very small, so almost all edges have the (second) maximum possible contribution to <span><math><mi>σ</mi></math></span>-irregularity. We believe this property or similar should extend to maximal trees for any value of <span><math><mi>Δ</mi></math></span>, so this is an interesting direction for further research.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"382 ","pages":"Pages 124-136"},"PeriodicalIF":1.0,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

(t,r)-Broadcast Domination in graphs （t,r）-图中的广播支配

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2025-12-16 DOI: 10.1016/j.dam.2025.12.024

Gennaro Cordasco, Luisa Gargano, Adele A. Rescigno

{"title":"(t,r)-Broadcast Domination in graphs","authors":"Gennaro Cordasco, Luisa Gargano, Adele A. Rescigno","doi":"10.1016/j.dam.2025.12.024","DOIUrl":"10.1016/j.dam.2025.12.024","url":null,"abstract":"<div><div>This paper explores a recently introduced graph problem called (<span><math><mrow><mi>t</mi><mo>,</mo><mi>r</mi></mrow></math></span>)-<span>Broadcast Domination</span>. In this problem, a set of “broadcasting” towers transmit a signal of initial strength <span><math><mi>t</mi></math></span>. This signal’s strength decreases linearly along the edges. The objective is to find the smallest set of broadcasting towers such that every vertex in the graph receives a cumulative signal strength of at least <span><math><mi>r</mi></math></span>. The (<span><math><mrow><mi>t</mi><mo>,</mo><mi>r</mi></mrow></math></span>)-<span>Broadcast Domination</span> problem, which generalizes the concept of distance domination, has been recently introduced and studied in a few specific class of graphs, like grids and lattices. However, the (<span><math><mrow><mi>t</mi><mo>,</mo><mi>r</mi></mrow></math></span>)-<span>Broadcast Domination</span> problem has not been studied for general graphs. We present the first study of the complexity of this problem in general graphs, including a general approximation algorithm and optimal polynomial-time algorithms for cographs. We also provide an algorithm parameterized by the neighborhood diversity of the input graph and an algorithm parameterized by modular-width and the solution size.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"382 ","pages":"Pages 355-367"},"PeriodicalIF":1.0,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Selected topics from the theory of intersections of balls 选自球的交点理论的题目

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2025-11-24 DOI: 10.1016/j.dam.2025.11.040

Károly Bezdek , Zsolt Lángi , Márton Naszódi

{"title":"Selected topics from the theory of intersections of balls","authors":"Károly Bezdek , Zsolt Lángi , Márton Naszódi","doi":"10.1016/j.dam.2025.11.040","DOIUrl":"10.1016/j.dam.2025.11.040","url":null,"abstract":"<div><div>In this survey, we discuss volumetric and combinatorial results concerning (mostly finite) intersections or unions of balls (mostly of equal radii) in the <span><math><mi>d</mi></math></span>-dimensional real vector space, mostly equipped with the Euclidean norm. Our first topic is the <em>Kneser–Poulsen Conjecture</em>, according to which if a finite number of balls are rearranged so that the pairwise distances of the centers increase, then the volume of the union (resp., intersection) increases (resp., decreases).</div><div>Next, we discuss Blaschke–Santaló-type inequalities, and reverse isoperimetric inequalities for convex sets in Euclidean <span><math><mi>d</mi></math></span>-space obtained as intersections of (possibly infinitely many) balls of radius <span><math><mi>r</mi></math></span>, which we call <span><math><mi>r</mi></math></span>-<em>ball bodies</em>. We present some results on 1-ball bodies (also called <em>ball-bodies</em> or <em>spindle convex sets</em>) in the plane, with special attention paid to their approximation by the spindle convex hull of a finite subset.</div><div>A <em>ball-polyhedron</em> is a ball-body obtained as the intersection of finitely many unit balls in Euclidean <span><math><mi>d</mi></math></span>-space. We consider the combinatorial structure of their faces, and volumetric properties of ball-polyhedra obtained from choosing the centers of the balls randomly.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"382 ","pages":"Pages 60-82"},"PeriodicalIF":1.0,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The directed pendant-tree 3-connectivity of symmetric compositions 对称组合的有向垂坠树3连通性

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2025-11-20 DOI: 10.1016/j.dam.2025.11.041

Shanshan Yu, Yuefang Sun

引用次数: 0

On the treewidth of token and Johnson graphs 关于令牌图和约翰逊图的树宽

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2025-11-21 DOI: 10.1016/j.dam.2025.11.042

Ruy Fabila-Monroy , Sergio Gerardo Gómez-Galicia , César Hernández-Cruz , Ana Trujillo-Negrete

引用次数: 0

Bip-ordered bipartite Ramsey number 双序二部拉姆齐数

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2025-12-12 DOI: 10.1016/j.dam.2025.12.010

Ayun Zhang , Baoleer , Shinya Fujita , Yaping Mao , Gang Yang

引用次数: 0

A multivariate complexity analysis of the Generalized Noah’s Ark Problem 广义诺亚方舟问题的多元复杂性分析

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2025-11-27 DOI: 10.1016/j.dam.2025.11.037

Christian Komusiewicz , Jannik Schestag

引用次数: 0

Bounds on broadcast time in well-connected graphs 良好连通图中广播时间的边界

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2025-11-24 DOI: 10.1016/j.dam.2025.11.013

Ararat Harutyunyan , Hovhannes A. Harutyunyan , Aram Khanlari

{"title":"Bounds on broadcast time in well-connected graphs","authors":"Ararat Harutyunyan , Hovhannes A. Harutyunyan , Aram Khanlari","doi":"10.1016/j.dam.2025.11.013","DOIUrl":"10.1016/j.dam.2025.11.013","url":null,"abstract":"<div><div>Given a graph <span><math><mi>G</mi></math></span>, the <em>broadcast time</em> <span><math><mrow><mi>b</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> of <span><math><mi>G</mi></math></span> is the least number of time units required to disseminate one piece of information starting at an arbitrary originating vertex in <span><math><mi>G</mi></math></span>, where each transmission takes one time unit and each informed vertex can transmit the message to one of its neighbors at any time. We initiate the study of finding upper bounds on broadcast time <span><math><mrow><mi>b</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> in highly connected graphs. In particular, we give upper bounds on <span><math><mrow><mi>b</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> for <span><math><mi>k</mi></math></span>-connected graphs and graphs with a large minimum degree. We prove that <span><math><mrow><mi>b</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mrow><mo>⌈</mo><mo>log</mo><mi>k</mi><mo>⌉</mo></mrow><mo>+</mo><mrow><mo>⌈</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></mfrac><mo>⌉</mo></mrow><mo>−</mo><mn>1</mn></mrow></math></span> for all <span><math><mi>k</mi></math></span>-connected graphs. For many families of graphs this bound is tight. We also show that if the minimum degree of <span><math><mi>G</mi></math></span> is at least <span><math><mrow><mi>n</mi><mo>/</mo><mn>2</mn></mrow></math></span>, then <span><math><mrow><mi>b</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mrow><mo>⌈</mo><mo>log</mo><mi>n</mi><mo>⌉</mo></mrow><mo>+</mo><mn>3</mn></mrow></math></span>, and derive various similar upper bounds on graphs with large minimum degree. Finally, we discuss an open problem that relates the broadcast time of a graph with its minimum degree, when the latter is small.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"382 ","pages":"Pages 83-90"},"PeriodicalIF":1.0,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Editorial: 10th International Conference on Algorithms and Discrete Applied Mathematics (CALDAM 2024) 第10届算法与离散应用数学国际会议（CALDAM 2024）

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2026-01-21 DOI: 10.1016/j.dam.2026.01.030

Subrahmanyam Kalyanasundaram, Anil Maheshwari

引用次数: 0

Maximum bond incident degree indices for trees and unicyclic graphs with given maximum degree 给定最大度的树和单环图的最大键关联度指标

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2026-03-31 Epub Date: 2025-12-12 DOI: 10.1016/j.dam.2025.12.021

Ioan Tomescu

引用次数: 0