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Minimum atom-bond sum-connectivity index of unicyclic graphs with maximum degree 最大阶数单环图的最小原子键和连通性指数
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-06 DOI: 10.47443/dml.2023.191
Palaniyappan Nithya, S. Elumalai, Selvaraj Balachandran
{"title":"Minimum atom-bond sum-connectivity index of unicyclic graphs with maximum degree","authors":"Palaniyappan Nithya, S. Elumalai, Selvaraj Balachandran","doi":"10.47443/dml.2023.191","DOIUrl":"https://doi.org/10.47443/dml.2023.191","url":null,"abstract":"Let G be a graph with edge set E ( G ) . Denote by d u the degree of a vertex u in G . The atom-bond sum-connectivity (ABS) index of G is defined as ABS ( G ) = (cid:80) xy ∈ E ( G ) (cid:112) ( d x + d y − 2) / ( d x + d y ) . In this article, we determine the minimum possible value of the ABS index of unicyclic graphs of order n and maximum degree ∆ such that 3 ≤ ∆ ≤ n − 2 . All the graphs that attain the obtained minimum value are also characterized.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140735002","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 number of spanning trees in a superprism 超prism 的生成树数量
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-05 DOI: 10.47443/dml.2024.004
Z. R. Bogdanowicz
{"title":"The number of spanning trees in a superprism","authors":"Z. R. Bogdanowicz","doi":"10.47443/dml.2024.004","DOIUrl":"https://doi.org/10.47443/dml.2024.004","url":null,"abstract":"Let the vertices of two disjoint and equal length cycles be denoted u 0 , u 1 , . . . , u n − 1 in the first cycle and v 0 , v 1 , . . . , v n − 1 in the second cycle for n ≥ 4 . The superprism ˘ P n is defined as the graph obtained by adding to these disjoint cycles all edges of the form u i v i and u i v i +2 (mod n ) . In this paper, it is proved that the number of spanning trees in ˘ P n is n · 2 3 n − 2 .","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140739796","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
All-path convexity: two characterizations, general position number, and one algorithm 全路径凸性：两个特征、一般位置数和一种算法
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-05 DOI: 10.47443/dml.2024.014
{"title":"All-path convexity: two characterizations, general position number, and one algorithm","authors":"","doi":"10.47443/dml.2024.014","DOIUrl":"https://doi.org/10.47443/dml.2024.014","url":null,"abstract":"We present two characterizations for the all-path convex sets in graphs. Using the first criterion, we obtain a new characterization of connected block graphs and compute the general position number in a graph with respect to the all-path convexity. The second criterion allows us to provide a new algorithm for testing a set on all-path convexity.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140737113","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
Linear vector recursions of arbitrary order 任意阶的线性矢量递推
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-05 DOI: 10.47443/dml.2024.029
Bernadette Faye, L´aszl´o N´emeth, L'aszl'o Szalay
{"title":"Linear vector recursions of arbitrary order","authors":"Bernadette Faye, L´aszl´o N´emeth, L'aszl'o Szalay","doi":"10.47443/dml.2024.029","DOIUrl":"https://doi.org/10.47443/dml.2024.029","url":null,"abstract":"Solution of various combinatorial problems often requires vector recurrences of higher order (i.e., the order is larger than 1). Assume that there are given matrices A 1 , A 2 , . . . , A s , all from C k × k . These matrices allow us to define the vector recurrence ¯ v n = A 1 ¯ v n − 1 + A 2 ¯ v n − 2 + · · · + A s ¯ v n − s for the vectors ¯ v n ∈ C k , n ≥ s . The paramount result of this paper is that we could separate the component sequences of the vectors and find a common linear recurrence relation to describe them. The principal advantage of our approach is a uniform treatment and the possibility of automatism. We could apply the main result to answer a problem that arose concerning the rows of the modified hyperbolic Pascal triangle with parameters { 4 , 5 } . We also verified two other statements from the literature in order to illustrate the power of the method.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140737160","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
Bargraphs of combinations with repetition 有重复的组合条形图
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-04 DOI: 10.47443/dml.2023.124
A. Blecher, A. Knopfmacher
{"title":"Bargraphs of combinations with repetition","authors":"A. Blecher, A. Knopfmacher","doi":"10.47443/dml.2023.124","DOIUrl":"https://doi.org/10.47443/dml.2023.124","url":null,"abstract":"Generating functions that track some geometrical features of combinations with repetition are developed; namely, the semi-perimeter, inner site-perimeter, and outer site-perimeter, each of whose meanings depends on the interpretation of the combination as a bargraph. The paper has three theorems, which respectively give the total number for each of these statistics based on separate generating functions tracking these statistics","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140743209","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
Independent domination polynomial for the cozero divisor graph of the ring of integers modulo n 整数环 modulo n 的 cozero 除数图的独立支配多项式
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-04 DOI: 10.47443/dml.2023.215
B. Rather
{"title":"Independent domination polynomial for the cozero divisor graph of the ring of integers modulo n","authors":"B. Rather","doi":"10.47443/dml.2023.215","DOIUrl":"https://doi.org/10.47443/dml.2023.215","url":null,"abstract":"The cozero divisor graph Γ (cid:48) ( R ) of a commutative ring R is a simple graph whose vertex set is the set of non-zero non-unit elements of R such that two distinct vertices x and y of Γ (cid:48) ( R ) are adjacent if and only if x / ∈ Ry and y / ∈ Rx , where Rx is the ideal generated by x . In this article, the independent domination polynomial of Γ (cid:48) ( Z n ) is found for n ∈ { p 1 p 2 , p 1 p 2 p 3 , p n 1 1 p 2 } , where p i ’s are primes, n 1 is an integer greater than 1 , and Z n is the integer modulo ring. It is shown that the independent domination polynomial of Γ (cid:48) ( Z p 1 p 2 ) has only one real root. It is also proved that these polynomials are not unimodal but are log-concave under certain conditions.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140745947","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 necessary conditions for graphs with extremal connected 2-domination number 具有极值连通 2-domination 数的图的一些必要条件
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-04 DOI: 10.47443/dml.2023.230
Piyawat Wongthongcue, Chalermpong Worawannotai
{"title":"Some necessary conditions for graphs with extremal connected 2-domination number","authors":"Piyawat Wongthongcue, Chalermpong Worawannotai","doi":"10.47443/dml.2023.230","DOIUrl":"https://doi.org/10.47443/dml.2023.230","url":null,"abstract":"Let G be a graph with no multiple edges and loops. A subset S of the vertex set of G is a dominating set of G if every vertex in V ( G ) S is adjacent to at least one vertex of S . A connected k -dominating set of G is a subset S of the vertex set V ( G ) such that every vertex in V ( G ) S has at least k neighbors in S and the subgraph G [ S ] is connected. The domination number of G is the number of vertices in a minimum dominating set of G , denoted by γ ( G ) . The connected k -domination number of G , denoted by γ ck ( G ) , is the minimum cardinality of a connected k -dominating set of G . For k = 1 , we simply write γ c ( G ) . It is known that the bounds γ c 2 ( G ) (cid:62) γ ( G ) + 1 and γ c 2 ( G ) (cid:62) γ c ( G ) + 1 are sharp. In this research article, we present the necessary condition of the connected graphs G with γ c 2 ( G ) = γ ( G ) + 1 and the necessary condition of the connected graphs G with γ c 2 ( G ) = γ c ( G )+1 . Moreover, we present a graph construction that takes in any connected graph with r vertices and gives a graph G with γ c 2 ( G ) = r , γ c ( G ) = r − 1 , and γ ( G ) ∈ { r − 1 , r −","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140741162","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 total number of descents and levels in (cyclic) tensor words 张量词（循环）中的降序和级别总数
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-04 DOI: 10.47443/dml.2023.218
S. Fried, Toufik Mansour
{"title":"The total number of descents and levels in (cyclic) tensor words","authors":"S. Fried, Toufik Mansour","doi":"10.47443/dml.2023.218","DOIUrl":"https://doi.org/10.47443/dml.2023.218","url":null,"abstract":"We obtain an explicit formula for the total number of descents and levels in (cyclic) tensor words of arbitrary dimension. We also determine the maximal number of cyclic descents in cyclic tensor words. Furthermore, we establish a lower bound and an upper bound on the maximal number of descents in tensor words","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140744288","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
Combinatorial identities and hypergeometric functions, II 组合等式和超几何函数，II
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-03 DOI: 10.47443/dml.2023.211
Horst Alzer
{"title":"Combinatorial identities and hypergeometric functions, II","authors":"Horst Alzer","doi":"10.47443/dml.2023.211","DOIUrl":"https://doi.org/10.47443/dml.2023.211","url":null,"abstract":"Properties of the classical Gaussian hypergeometric function are applied to prove some combinatorial identities. Among others, a corrected and simplified version of a formula of D. Lim [ Notes Number Theory","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140748515","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
Trails in arc-colored digraphs avoiding forbidden transitions 避免禁止转换的弧色数字图中的轨迹
IF 0.8
Discrete Mathematics Letters Pub Date : 2024-04-03 DOI: 10.47443/dml.2023.190
Carlos Vilchis-Alfaro, Hortensia Galeana-S´anchez
{"title":"Trails in arc-colored digraphs avoiding forbidden transitions","authors":"Carlos Vilchis-Alfaro, Hortensia Galeana-S´anchez","doi":"10.47443/dml.2023.190","DOIUrl":"https://doi.org/10.47443/dml.2023.190","url":null,"abstract":"Let H be a digraph possibly with loops. Let D be a digraph without loops. An H -coloring of D is a function c : A ( D ) → V ( H ) . We say that D is an H -colored digraph whenever we are taking a fixed H -coloring of D . A trail W = ( v 0 , e 0 , v 1 , e 1 , v 2 , . . . , v n − 1 , e n − 1 , v n ) in D is an H -trail if and only if ( c ( e i ) , c ( e i +1 )) is an arc in H for every i ∈ { 0 , . . . , n − 2 } . Whenever the vertices of an H -trail are pairwise different, we say that it is an H -path. In this paper, we study the problem of finding s − t H -trail in H -colored digraphs. First, we prove that finding an H -trail starting with the arc e and ending at arc f can be done in polynomial time. As a consequence, we give a polynomial time algorithm to find the shortest H -trail from a vertex s to a vertex t (if it exists). Moreover, we obtain a Menger-type theorem for H -trails. As a consequence, we show that the problem of maximizing the number of arc disjoint s − t H -trails in D can be solved in polynomial time. Although finding an H -path between two given vertices is an NP-problem, it becomes a polynomial time problem in the case when H is a reflexive and transitive digraph.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140746656","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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