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On the permutation cycle structures for almost Moore digraphs of degrees 4 and 5 论4度和5度几乎摩尔数图的置换循环结构
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-12-21 DOI: 10.47443/dml.2023.142
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引用次数: 0
Atom-bond sum-connectivity index of line graphs 线图的原子键和连接指数
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-12-21 DOI: 10.47443/dml.2023.197
{"title":"Atom-bond sum-connectivity index of line graphs","authors":"","doi":"10.47443/dml.2023.197","DOIUrl":"https://doi.org/10.47443/dml.2023.197","url":null,"abstract":"","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138953157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
General sum-connectivity index and general Randic index of trees with given maximum degree 给定最大树度的树的一般总连接指数和一般兰迪克指数
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-12-11 DOI: 10.47443/dml.2023.140
Elize Swartz, Tom´aˇs Vetr´ık
{"title":"General sum-connectivity index and general Randic index of trees with given maximum degree","authors":"Elize Swartz, Tom´aˇs Vetr´ık","doi":"10.47443/dml.2023.140","DOIUrl":"https://doi.org/10.47443/dml.2023.140","url":null,"abstract":"For trees with given number of vertices n and maximum degree ∆ , we present lower bounds on the general sum-connectivity index χ a if a > 0 and 3 ≤ ∆ ≤ n − 1 , and an upper bound on the general Randi´c index R a if − 0 . 283 ≤ a < 0 and 3 ≤ ∆ ≤ (cid:98) n − 1 2 (cid:99) . All the extremal trees for our bounds are given.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139010369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The b$_q$-coloring of graphs 图形的 b$_q$ 着色
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-11-27 DOI: 10.47443/dml.2023.098
{"title":"The b$_q$-coloring of graphs","authors":"","doi":"10.47443/dml.2023.098","DOIUrl":"https://doi.org/10.47443/dml.2023.098","url":null,"abstract":"","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139233299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extremal trees with fixed degree sequence for $sigma$-irregularity 针对 $sigma$-irregularity 的具有固定阶序的极值树
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-11-27 DOI: 10.47443/dml.2023.106
{"title":"Extremal trees with fixed degree sequence for $sigma$-irregularity","authors":"","doi":"10.47443/dml.2023.106","DOIUrl":"https://doi.org/10.47443/dml.2023.106","url":null,"abstract":"","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139233244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Counterexamples to the total vertex irregularity strength’s conjectures 总顶点不规则强度猜想的反例
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-11-27 DOI: 10.47443/dml.2023.111
Faisal Susanto, R. Simanjuntak, E. Baskoro
{"title":"Counterexamples to the total vertex irregularity strength’s conjectures","authors":"Faisal Susanto, R. Simanjuntak, E. Baskoro","doi":"10.47443/dml.2023.111","DOIUrl":"https://doi.org/10.47443/dml.2023.111","url":null,"abstract":"The total vertex irregularity strength tvs( G ) of a simple graph G ( V, E ) is the smallest positive integer k so that there exists a function ϕ : V ∪ E → [1 , k ] provided that all vertex-weights are distinct, where a vertex-weight is the sum of labels of a vertex and all of its incident edges. In the paper [Nurdin, E. T. Baskoro, A. N. M. Salman, N. N. Gaos, Discrete Math. 310 (2010) 3043–3048], two conjectures regarding the total vertex irregularity strength of trees and general graphs were posed as follows: (i) for every tree T , tvs( T ) = max {(cid:100) ( n 1 + 1) / 2 (cid:101) , (cid:100) ( n 1 + n 2 + 1) / 3 (cid:101) , (cid:100) ( n 1 + n 2 + n 3 + 1) / 4 (cid:101)} , and (ii) for every graph G with minimum degree δ and maximum degree ∆ , tvs( G ) = max {(cid:100) ( δ + (cid:80) i j =1 n j ) / ( i + 1) (cid:101) : i ∈ [ δ, ∆] } , where n j denotes the number of vertices of degree j . In this paper, we disprove both of these conjectures by giving infinite families of counterexamples.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139234445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Permutations avoiding the complement of a regular permutation group 避免正则置换群补的置换
Discrete Mathematics Letters Pub Date : 2023-11-13 DOI: 10.47443/dml.2023.141
{"title":"Permutations avoiding the complement of a regular permutation group","authors":"","doi":"10.47443/dml.2023.141","DOIUrl":"https://doi.org/10.47443/dml.2023.141","url":null,"abstract":"The class of permutations avoiding the complement of an arbitrary regular permutation group is described.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136346313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some results about ID-path-factor critical graphs 关于id -路径-因子关键图的一些结果
Discrete Mathematics Letters Pub Date : 2023-11-13 DOI: 10.47443/dml.2023.131
{"title":"Some results about ID-path-factor critical graphs","authors":"","doi":"10.47443/dml.2023.131","DOIUrl":"https://doi.org/10.47443/dml.2023.131","url":null,"abstract":"Let G be a graph of order n . A spanning subgraph F of G is said to be a P ≥ k -factor of G if every component of F is a path with at least k vertices, where k ≥ 2 . In this paper, we introduce the concept of an ID-P ≥ k -factor critical graph; a graph G is said to be an ID-P ≥ k -factor critical graph if for any independent set I of G , G − I admits a P ≥ k -factor. We prove that a graph G of a given order is an ID-P ≥ 2 -factor critical graph if its binding number is at least 2 . We also prove that a graph G of a fixed order is an ID-P ≥ 3 -factor critical graph if its binding number is at least 94 . Furthermore, we show that the obtained results are the best possible in some sense.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136348549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The multicolor star-critical Gallai-Ramsey number for a path of order 5 5阶路径的多色星临界加莱-拉姆齐数
Discrete Mathematics Letters Pub Date : 2023-10-17 DOI: 10.47443/dml.2023.115
{"title":"The multicolor star-critical Gallai-Ramsey number for a path of order 5","authors":"","doi":"10.47443/dml.2023.115","DOIUrl":"https://doi.org/10.47443/dml.2023.115","url":null,"abstract":"In this paper, the t -color star-critical Gallai-Ramsey number for a path of order 5 is determined. It is proved that t +1 edges are both necessary and sufficient to add between a vertex and a critical coloring for the t -color Gallai-Ramsey number for P 5 in order to guarantee the existence of a monochromatic subgraph isomorphic to P 5 . The proof depends on a well-known structural result for Gallai colorings as well as a general lower bound due to Faudree, Gould, Jacobson, and Magnant.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136032906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On zonal and inner zonal labelings of plane graphs of maximum degree 3 关于最大度为3的平面图的区域标记和内区域标记
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-08-25 DOI: 10.47443/dml.2023.083
Andrew Bowling, Ping Zhang
{"title":"On zonal and inner zonal labelings of plane graphs of maximum degree 3","authors":"Andrew Bowling, Ping Zhang","doi":"10.47443/dml.2023.083","DOIUrl":"https://doi.org/10.47443/dml.2023.083","url":null,"abstract":"A zonal labeling of a plane graph G is an assignment of the two nonzero elements of the ring Z 3 of integers modulo 3 to the vertices of G such that the sum of the labels of the vertices on the boundary of each region of G is the zero element of Z 3 . A plane graph possessing such a labeling is a zonal graph. If there is at most one exception, then the labeling is inner zonal and the graph is inner zonal. In 2019, Chartrand, Egan, and Zhang proved that showing the existence of zonal labelings in all cubic maps is equivalent to giving a proof of the Four Color Theorem. It is shown that every inner zonal cubic map is zonal, thereby establishing an improvement of the 2019 result. It is also shown that (i) while certain 2 -connected plane graphs of maximum degree 3 may not be zonal, they must be inner zonal and (ii) no connected cubic plane graph with bridges can be inner zonal.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48042922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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