Let G be a simple graph with the vertex set V ( G ) and edge set E ( G ) . Let d G ( v i ) be the degree of the vertex v i ∈ V ( G ) . A vertex-degree-based topological index (TI) of G is defined as TI ( G ) = (cid:80)
{"title":"On the minimum and second-minimum values of degree-based energies for trees","authors":"Yanjie Fu, Yubin Gao","doi":"10.47443/cm.2023.047","DOIUrl":"https://doi.org/10.47443/cm.2023.047","url":null,"abstract":"Let G be a simple graph with the vertex set V ( G ) and edge set E ( G ) . Let d G ( v i ) be the degree of the vertex v i ∈ V ( G ) . A vertex-degree-based topological index (TI) of G is defined as TI ( G ) = (cid:80)","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136357759","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}
Based on the parallelogram law and orthogonality, we define a new geometric constant and obtain some of its geometric properties. This constant provides a useful tool for estimating the exact values of Jordan-von Neumann constants in Banach spaces and for studying the orthogonality. In addition, we consider Pythagorean orthogonality and introduce another new constant to investigate a connection between Pythagorean orthogonality and isosceles orthogonality
{"title":"Geometric constants and orthogonality in Banach spaces","authors":"Yin Zhou, Qichuan Ni, Qi Liu, Yongjin Li","doi":"10.47443/cm.2023.045","DOIUrl":"https://doi.org/10.47443/cm.2023.045","url":null,"abstract":"Based on the parallelogram law and orthogonality, we define a new geometric constant and obtain some of its geometric properties. This constant provides a useful tool for estimating the exact values of Jordan-von Neumann constants in Banach spaces and for studying the orthogonality. In addition, we consider Pythagorean orthogonality and introduce another new constant to investigate a connection between Pythagorean orthogonality and isosceles orthogonality","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135980215","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}
Given a graph G , many of its topological descriptors have the additive form D p ( G ) = (cid:80) i c pi , where the c i s are positive parameters associated with G , and p is an arbitrary real number. Sometimes these expressions are generalizations of descriptors with the simpler form D ( G ) = (cid:80) i c i . It is shown how Radon’s inequality and its refinements can be used to find a variety of bounds among members of these families of generalized descriptors. The particular case of sums of powers of normalized Laplacian eigenvalues is thoroughly discussed.
给定一个图G，它的许多拓扑描述符具有加性形式dp (G) = (cid:80) ci pi，其中ci s是与G相关的正参数，p是任意实数。有时，这些表达式是描述符的一般化，具有更简单的形式D (G) = (cid:80) i ci。它显示了Radon不等式及其改进如何可以用来找到这些广义描述符族的成员之间的各种界限。详细讨论了归一化拉普拉斯特征值幂和的特殊情况。
{"title":"Applications of Radon’s inequalities to generalized topological descriptors","authors":"J. Palacios","doi":"10.47443/cm.2023.036","DOIUrl":"https://doi.org/10.47443/cm.2023.036","url":null,"abstract":"Given a graph G , many of its topological descriptors have the additive form D p ( G ) = (cid:80) i c pi , where the c i s are positive parameters associated with G , and p is an arbitrary real number. Sometimes these expressions are generalizations of descriptors with the simpler form D ( G ) = (cid:80) i c i . It is shown how Radon’s inequality and its refinements can be used to find a variety of bounds among members of these families of generalized descriptors. The particular case of sums of powers of normalized Laplacian eigenvalues is thoroughly discussed.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81325759","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}
By means of the generating function method as well as Stirling and Lah inversion, several summation formulae involving generalized harmonic-like numbers and other combinatorial numbers named after Stirling, Lah, Hal and Fubini are derived.
{"title":"Formulae concerning multiple harmonic-like numbers","authors":"Yulei Chen, Dongwei Guo","doi":"10.47443/cm.2023.044","DOIUrl":"https://doi.org/10.47443/cm.2023.044","url":null,"abstract":"By means of the generating function method as well as Stirling and Lah inversion, several summation formulae involving generalized harmonic-like numbers and other combinatorial numbers named after Stirling, Lah, Hal and Fubini are derived.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89454189","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}
Paulo M. Guzman, J. N. Nápoles Valdés, Vuk Stojiljković
Some new results related to generalized Hermite-Hadamard-type inequalities are established. For obtaining new inequalities, various approaches are utilized, including boundedness, convexity, and concavity. Considering special values of the parameters, it is demonstrated how the obtained inequalities reduce to the known ones
{"title":"New extensions of the Hermite-Hadamard inequality","authors":"Paulo M. Guzman, J. N. Nápoles Valdés, Vuk Stojiljković","doi":"10.47443/cm.2023.032","DOIUrl":"https://doi.org/10.47443/cm.2023.032","url":null,"abstract":"Some new results related to generalized Hermite-Hadamard-type inequalities are established. For obtaining new inequalities, various approaches are utilized, including boundedness, convexity, and concavity. Considering special values of the parameters, it is demonstrated how the obtained inequalities reduce to the known ones","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79885772","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}
Luiz Gutemberg Rosário Miranda, C. Raposo, S. Cordeiro
This article focuses on a Timoshenko beam model introduced by Elishakoff. This model is free of the second frequency spectrum and solves the paradox of equal wave speeds, related to Timoshenko’s model. Damping created by a fractional Laplacian is considered, which includes internal damping, Kelvin-Voigt damping, and intermediate damping. Exponential stability is shown without requiring any relationship between the system coefficients
{"title":"Truncated Bresse-Timoshenko beam with fractional Laplacian damping","authors":"Luiz Gutemberg Rosário Miranda, C. Raposo, S. Cordeiro","doi":"10.47443/cm.2023.031","DOIUrl":"https://doi.org/10.47443/cm.2023.031","url":null,"abstract":"This article focuses on a Timoshenko beam model introduced by Elishakoff. This model is free of the second frequency spectrum and solves the paradox of equal wave speeds, related to Timoshenko’s model. Damping created by a fractional Laplacian is considered, which includes internal damping, Kelvin-Voigt damping, and intermediate damping. Exponential stability is shown without requiring any relationship between the system coefficients","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77974005","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}
The second-smallest eigenvalue of the Laplacian matrix of a graph G is called the algebraic connectivity of G , which is one of the most-studied parameters in spectral graph theory and network science. In this paper, we obtain some new lower bounds of the algebraic connectivity by rank-one perturbation matrix and compare them with known results.
{"title":"Some New Lower Bounds on the Algebraic Connectivity of Graphs","authors":"Zhen Lin, Rong Zhang, Juan Wang","doi":"10.47443/cm.2023.016","DOIUrl":"https://doi.org/10.47443/cm.2023.016","url":null,"abstract":"The second-smallest eigenvalue of the Laplacian matrix of a graph G is called the algebraic connectivity of G , which is one of the most-studied parameters in spectral graph theory and network science. In this paper, we obtain some new lower bounds of the algebraic connectivity by rank-one perturbation matrix and compare them with known results.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73800296","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}
In this article, new bounds for the mean and the variance of uniformly distributed discrete random variables are derived. It is shown that the new results, under certain conditions, are better than the bounds of Bhatia and Davies reported in [ Amer. Math. Monthly 107 (2000) 353–357].
{"title":"New Bounds for the Mean and the Variance","authors":"S. Filipovski","doi":"10.47443/cm.2023.005","DOIUrl":"https://doi.org/10.47443/cm.2023.005","url":null,"abstract":"In this article, new bounds for the mean and the variance of uniformly distributed discrete random variables are derived. It is shown that the new results, under certain conditions, are better than the bounds of Bhatia and Davies reported in [ Amer. Math. Monthly 107 (2000) 353–357].","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80301627","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}
Yukio Takahashi, Rikio Ichishima, F. Muntaner-Batle
A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $left{ 1,2,ldots ,nright} $ to the vertices of $G$. The strength $textrm{str}_{f}left( Gright)$ of a numbering $f:Vleft( Gright) rightarrow left{ 1,2,ldots ,nright} $ of $G$ is defined by% begin{equation*} mathrm{str}_{f}left( Gright) =max left{ fleft( uright) +fleft( vright) left| uvin Eleft( Gright) right. right} text{,} end{equation*}% that is, $mathrm{str}_{f}left( Gright) $ is the maximum edge label of $G$ and the strength textrm{str}$left( Gright) $ of a graph $G$ itself is begin{equation*} mathrm{str}left( Gright) =min left{ mathrm{str}_{f}left( Gright) left| ftext{ is a numbering of }Gright. right} text{.} end{equation*} In this paper, we present a sharp lower bound for the strength of a graph in terms of its domination number as well as its (edge) covering and (edge) independence number. We also provide a necessary and sufficient condition for the strength of a graph to attain the earlier bound in terms of their subgraph structure. In addition, we establish a sharp lower bound for the domination number of a graph under certain conditions.
顺序为$n$的图$G$的编号$f$是一个标记，它将集合$left{ 1,2,ldots ,nright} $的不同元素分配给$G$的顶点。编号$f:Vleft( Gright) rightarrow left{ 1,2,ldots ,nright} $$G$的强度$textrm{str}_{f}left( Gright)$定义为% begin{equation*} mathrm{str}_{f}left( Gright) =max left{ fleft( uright) +fleft( vright) left| uvin Eleft( Gright) right. right} text{,} end{equation*}% that is, $mathrm{str}_{f}left( Gright) $ is the maximum edge label of $G$ and the strength textrm{str}$left( Gright) $ of a graph $G$ itself is begin{equation*} mathrm{str}left( Gright) =min left{ mathrm{str}_{f}left( Gright) left| ftext{ is a numbering of }Gright. right} text{.} end{equation*} In this paper, we present a sharp lower bound for the strength of a graph in terms of its domination number as well as its (edge) covering and (edge) independence number. We also provide a necessary and sufficient condition for the strength of a graph to attain the earlier bound in terms of their subgraph structure. In addition, we establish a sharp lower bound for the domination number of a graph under certain conditions.
{"title":"On the strength and domination number of graphs","authors":"Yukio Takahashi, Rikio Ichishima, F. Muntaner-Batle","doi":"10.47443/cm.2023.020","DOIUrl":"https://doi.org/10.47443/cm.2023.020","url":null,"abstract":"A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $left{ 1,2,ldots ,nright} $ to the vertices of $G$. The strength $textrm{str}_{f}left( Gright)$ of a numbering $f:Vleft( Gright) rightarrow left{ 1,2,ldots ,nright} $ of $G$ is defined by% begin{equation*} mathrm{str}_{f}left( Gright) =max left{ fleft( uright) +fleft( vright) left| uvin Eleft( Gright) right. right} text{,} end{equation*}% that is, $mathrm{str}_{f}left( Gright) $ is the maximum edge label of $G$ and the strength textrm{str}$left( Gright) $ of a graph $G$ itself is begin{equation*} mathrm{str}left( Gright) =min left{ mathrm{str}_{f}left( Gright) left| ftext{ is a numbering of }Gright. right} text{.} end{equation*} In this paper, we present a sharp lower bound for the strength of a graph in terms of its domination number as well as its (edge) covering and (edge) independence number. We also provide a necessary and sufficient condition for the strength of a graph to attain the earlier bound in terms of their subgraph structure. In addition, we establish a sharp lower bound for the domination number of a graph under certain conditions.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91157763","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}
The Gaussian Leonardo sequence is a new sequence defined in this study. Some identities for this new sequence are given. Some relations among the Gaussian Fibonacci numbers, Gaussian Lucas numbers, and Gaussian Leonardo numbers are also proven. Moreover, a matrix representation of the Gaussian Leonardo numbers is obtained.
{"title":"On Gaussian Leonardo Numbers","authors":"Dursun Tas¸cı","doi":"10.47443/cm.2022.064","DOIUrl":"https://doi.org/10.47443/cm.2022.064","url":null,"abstract":"The Gaussian Leonardo sequence is a new sequence defined in this study. Some identities for this new sequence are given. Some relations among the Gaussian Fibonacci numbers, Gaussian Lucas numbers, and Gaussian Leonardo numbers are also proven. Moreover, a matrix representation of the Gaussian Leonardo numbers is obtained.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80578996","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}
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