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On a Conjecture Regarding the Exponential Reduced Sombor Index of Chemical Trees 关于化学树指数化简Sombor指数的一个猜想
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-05-19 DOI: 10.47443/dml.2021.s217
A. Hamza, Akbar Ali
{"title":"On a Conjecture Regarding the Exponential Reduced Sombor Index of Chemical Trees","authors":"A. Hamza, Akbar Ali","doi":"10.47443/dml.2021.s217","DOIUrl":"https://doi.org/10.47443/dml.2021.s217","url":null,"abstract":"Let G be a graph and denote by du the degree of a vertex u of G. The sum of the numbers e √ (du−1)+(dv−1) over all edges uv of G is known as the exponential reduced Sombor index. A chemical tree is a tree with the maximum degree at most 4. In this paper, a conjecture posed by Liu et al. [MATCH Commun. Math. Comput. Chem. 86 (2021) 729–753] is disproved and its corrected version is proved.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46941109","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: 2
Odd Facial Total-Coloring of Unicyclic Plane Graphs 单环平面图的奇面全着色
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-05-16 DOI: 10.47443/dml.2022.022
J. Czap
{"title":"Odd Facial Total-Coloring of Unicyclic Plane Graphs","authors":"J. Czap","doi":"10.47443/dml.2022.022","DOIUrl":"https://doi.org/10.47443/dml.2022.022","url":null,"abstract":"A facial total-coloring of a plane graph G is a coloring of the vertices and edges such that no facially adjacent edges (edges that are consecutive on the boundary walk of a face of G ), no adjacent vertices, and no edge and its endvertices are assigned the same color. A facial total-coloring of G is odd if for every face f and every color c , either no element or an odd number of elements incident with f is colored by c . In this paper, it is proved that every unicyclic plane graph admits an odd facial total-coloring with at most 10 colors. It is also shown that this bound is tight.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47315909","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
A Binomial Formula for Evaluating Integrals 求积分的二项式公式
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-05-16 DOI: 10.47443/dml.2022.013
K. Boyadzhiev
{"title":"A Binomial Formula for Evaluating Integrals","authors":"K. Boyadzhiev","doi":"10.47443/dml.2022.013","DOIUrl":"https://doi.org/10.47443/dml.2022.013","url":null,"abstract":"In this paper, a special formula for transforming integrals to series is presented. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging integrals.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41897946","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
Gallai-Ramsey Number for Rainbow S3 彩虹S3的Gallai Ramsey数
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-05-14 DOI: 10.47443/dml.2022.033
Reji Thankachan, Ruby Rosemary, Sneha Balakrishnan
{"title":"Gallai-Ramsey Number for Rainbow S3","authors":"Reji Thankachan, Ruby Rosemary, Sneha Balakrishnan","doi":"10.47443/dml.2022.033","DOIUrl":"https://doi.org/10.47443/dml.2022.033","url":null,"abstract":"For the given graphs G and H , and for a positive integer k , the Gallai-Ramsey number is denoted by gr k ( G : H ) and is defined as the minimum integer n such that every coloring of the complete graph K n using at most k colors contains either a rainbow copy of G or a monochromatic copy of H . The k -color Ramsey number for G , denoted by R k ( G ) , is the minimum integer n such that every coloring of K n using at most k colors contains a monochromatic copy of G in some color. Let S n be the star graph on n edges and let P n be the path graph on n vertices. Denote by S + n the graph obtained from S n by adding an edge between any two pendant vertices. Let T n +2 be the tree on n + 2 vertices obtained from S n by subdividing one of its edges. In this paper, we consider gr k ( S 3 : H ) , where H ∈ { S n , S + n , P n , T n +2 } , and obtain its relation with R 2 ( H ) and R 3 ( H ) . We also obtain 3 -color Ramsey numbers for S n , S + n , and T n +2 .","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47239736","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
Signed Total Strong Roman Domination in Graphs 在图形中签名的总强大罗马统治
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-05-12 DOI: 10.47443/dml.2022.020
M. Hajjari, S. M. Sheikholeslami
{"title":"Signed Total Strong Roman Domination in Graphs","authors":"M. Hajjari, S. M. Sheikholeslami","doi":"10.47443/dml.2022.020","DOIUrl":"https://doi.org/10.47443/dml.2022.020","url":null,"abstract":"Let G = ( V, E ) be a finite and simple graph of order n and maximum degree ∆ . A signed total strong Roman dominating function on G is a function f : V → {− 1 , 1 , 2 , . . . , (cid:100) ∆ / 2 (cid:101) + 1 } satisfying the conditions: (i) for every vertex v of G , (cid:80) u ∈ N ( v ) f ( u ) ≥ 1 , where N ( v ) is the open neighborhood of v , and (ii) every vertex v satisfying f ( v ) = − 1 is adjacent to at least one vertex u such that f ( u ) ≥ 1 + (cid:6) | N ( u ) ∩ V − 1 | / 2 (cid:7) , where V − 1 = { v ∈ V | f ( v ) = − 1 } . The signed total strong Roman domination number of G , γ tssR ( G ) , is the minimum weight of a signed total strong Roman dominating function. In this paper, some bounds for this parameter are presented.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43052408","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 Chromatic Vertex Stability of 3-Chromatic Graphs With Maximum Degree 4 关于最大度为4的3-色图的色顶点稳定性
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-05-04 DOI: 10.47443/dml.2022.066
M. Knor, Mirko Petruvsevski, Riste vSkrekovski
{"title":"On Chromatic Vertex Stability of 3-Chromatic Graphs With Maximum Degree 4","authors":"M. Knor, Mirko Petruvsevski, Riste vSkrekovski","doi":"10.47443/dml.2022.066","DOIUrl":"https://doi.org/10.47443/dml.2022.066","url":null,"abstract":"The (independent) chromatic vertex stability (ivs χ ( G )) vs χ ( G ) is the minimum size of (independent) set S ⊆ V ( G ) such that χ ( G − S ) = χ ( G ) − 1. In this paper we construct infinitely many graphs G with ∆( G ) = 4, χ ( G ) = 3, ivs χ ( G ) = 3 and vs χ ( G ) = 2, which gives a partial negative answer to a problem posed in [3].","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43158083","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
Product of conjugacy classes of complete cycles in the alternating group 交替群中完全环共轭类的乘积
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-04-30 DOI: 10.47443/dml.2022.018
Omar Tout
{"title":"Product of conjugacy classes of complete cycles in the alternating group","authors":"Omar Tout","doi":"10.47443/dml.2022.018","DOIUrl":"https://doi.org/10.47443/dml.2022.018","url":null,"abstract":"The product of conjugacy classes of a finite group can be written as a linear combination of conjugacy classes with integer coefficients. For the symmetric group, some explicit expressions for these coefficients are known only in particular cases. The aim of this paper is to give explicit expressions for the product of the conjugacy classes in the alternating group A n corresponding to cycles of length n .","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48508101","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
Distance Signless Laplacian Eigenvalues, Diameter, and Clique Number 距离无符号拉普拉斯特征值，直径和团数
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-04-19 DOI: 10.47443/dml.2022.010
Saleem Khan, S. Pirzada
{"title":"Distance Signless Laplacian Eigenvalues, Diameter, and Clique Number","authors":"Saleem Khan, S. Pirzada","doi":"10.47443/dml.2022.010","DOIUrl":"https://doi.org/10.47443/dml.2022.010","url":null,"abstract":"Let G be a connected graph of order n . Let D iag ( Tr ) be the diagonal matrix of vertex transmissions and let D ( G ) be the distance matrix of G . The distance signless Laplacian matrix of G is defined as D Q ( G ) = D iag ( Tr ) + D ( G ) and the eigenvalues of D Q ( G ) are called the distance signless Laplacian eigenvalues of G . Let ∂ Q 1 ( G ) ≥ ∂ Q 2 ( G ) ≥ · · · ≥ ∂ Q n ( G ) be the distance signless Laplacian eigenvalues of G . The largest eigenvalue ∂ Q 1 ( G ) is called the distance signless Laplacian spectral radius. We obtain a lower bound for ∂ Q 1 ( G ) in terms of the diameter and order of G . With a given interval I , denote by m D Q ( G ) I the number of distance signless Laplacian eigenvalues of G which lie in I . For a given interval I , we also obtain several bounds on m D Q ( G ) I in terms of various structural parameters of the graph G , including diameter and clique number.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45841968","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: 1
Trinajstić Index
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-04-19 DOI: 10.47443/dml.2021.s216
Boris Furtula
{"title":"Trinajstić Index","authors":"Boris Furtula","doi":"10.47443/dml.2021.s216","DOIUrl":"https://doi.org/10.47443/dml.2021.s216","url":null,"abstract":"Professor Trinajsti´c devoted years of research to deepen the knowledge of the distance–based topological indices. He was especially interested in so-called Szeged-type indices. Several such indices were introduced directly by himself, but none of them was named after him. In this paper, a novel topological invariant of this kind is proposed, and it is boldly named the Trinajsti´c index . The performed computational tests are justifying the introduction of this novel topological index.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44139765","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: 2
Padmakar-Ivan Index of Some Types of Perfect Graphs 几类完美图的Padmakar-Ivan指数
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-04-18 DOI: 10.47443/dml.2021.s215
Manju Sankaramalil Chithrabhanu, K. Somasundaram
{"title":"Padmakar-Ivan Index of Some Types of Perfect Graphs","authors":"Manju Sankaramalil Chithrabhanu, K. Somasundaram","doi":"10.47443/dml.2021.s215","DOIUrl":"https://doi.org/10.47443/dml.2021.s215","url":null,"abstract":"The Padmakar-Ivan (PI) index of a graph G is defined as PI ( G ) = (cid:80) e ∈ E ( G ) ( | V ( G ) | − N G ( e )) , where N G ( e ) is the number of equidistant vertices for the edge e . A graph is perfect if for every induced subgraph H , the equation χ ( H ) = ω ( H ) holds, where χ ( H ) is the chromatic number and ω ( H ) is the size of a maximum clique of H . In this paper, the PI index of some types of perfect graphs is obtained. These types include co-bipartite graphs, line graphs, and prismatic graphs.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41870828","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: 2
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