The atom-bond connectivity（ABC） index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes,which is defined as ABC（G） =∑ uv∈E（G） √d u＋dv-2 dudv,...The atom-bond connectivity（ABC） index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes,which is defined as ABC（G） =∑ uv∈E（G） √d u＋dv-2 dudv,where du denotes the degree of a vertex u in G.A chemical graph is a graph in which no vertex has degree greater than 4.In this paper,we obtain the sharp upper and lower bounds on ABC index of chemical bicyclic graphs.展开更多
图G(V,E)的邻点可约全标号(adjacent vertex reducible total labeling,AVRTL)是一个从V(G)∪E(G)到连续整数集{1,2,…,|V(G)|+|E(G)|}的双射,且图中所有相邻同度顶点的标号之和均相同,为S(u)=f(u)+∑uw∈E(G)f(uw).该文结合现实问题,...图G(V,E)的邻点可约全标号(adjacent vertex reducible total labeling,AVRTL)是一个从V(G)∪E(G)到连续整数集{1,2,…,|V(G)|+|E(G)|}的双射,且图中所有相邻同度顶点的标号之和均相同,为S(u)=f(u)+∑uw∈E(G)f(uw).该文结合现实问题,借鉴传统遗传算法、蜂群算法等智能算法思路,设计了一种新型的AVRTL算法,通过预处理函数、调整函数等,利用循环迭代寻优的方式得到有限点内所有双圈图的邻点可约全标号结果.对实验结果进行分析,发现几类图的标号规律,总结得到若干定理并给出证明,最后给出猜想:所有的双圈图均为AVRTL图.展开更多
In this paper,we determine graphs with the largest Laplacian spectral radius among the unicyclic and the bicyclic graphs on n vertices with k pendant vertices,respectively.
The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In our recent work, we have determined the graphs...The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In our recent work, we have determined the graphs with maximal Laplacian spreads among all trees of fixed order and among all unicyclic graphs of fixed order, respectively. In this paper, we continue the work on Laplacian spread of graphs, and prove that there exist exactly two bicyclic graphs with maximal Laplacian spread among all bicyclic graphs of fixed order, which are obtained from a star by adding two incident edges and by adding two nonincident edges between the pendant vertices of the star, respectively.展开更多
The spectral spread of a graph is defined to be the difference between the largest and the least eigenvalue of the adjacency matrix of the graph. A graph G is said to be bicyclic, if G is connected and ｜E（G）｜ = ...The spectral spread of a graph is defined to be the difference between the largest and the least eigenvalue of the adjacency matrix of the graph. A graph G is said to be bicyclic, if G is connected and ｜E（G）｜ = ｜V （G）｜ ＋ 1. Let B（n, g） be the set of bicyclic graphs on n vertices with girth g. In this paper some properties about the least eigenvalues of graphs are given, by which the unique graph with maximal spectral spread in B（n, g） is determined.展开更多
A graph G is nonsingular if its adjacency matrix A(G)is nonsingular.A nonsingular graph G is said to have an inverse G+if A(G)-1 is signature similar to a nonnegative matrix.Let H be the class of connected bipartite g...A graph G is nonsingular if its adjacency matrix A(G)is nonsingular.A nonsingular graph G is said to have an inverse G+if A(G)-1 is signature similar to a nonnegative matrix.Let H be the class of connected bipartite graphs with unique perfect matchings.We present a characterization of bicyclic graphs in H which possess unicyclic or bicyclic inverses.展开更多
基金Supported by the National Natural Science Foundation of China(11071272,10831001,11171279,11101087)the Young Talent Foundation of Fuzhou University(XRC-1154)
文摘The atom-bond connectivity（ABC） index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes,which is defined as ABC（G） =∑ uv∈E（G） √d u＋dv-2 dudv,where du denotes the degree of a vertex u in G.A chemical graph is a graph in which no vertex has degree greater than 4.In this paper,we obtain the sharp upper and lower bounds on ABC index of chemical bicyclic graphs.
文摘图G(V,E)的邻点可约全标号(adjacent vertex reducible total labeling,AVRTL)是一个从V(G)∪E(G)到连续整数集{1,2,…,|V(G)|+|E(G)|}的双射,且图中所有相邻同度顶点的标号之和均相同,为S(u)=f(u)+∑uw∈E(G)f(uw).该文结合现实问题,借鉴传统遗传算法、蜂群算法等智能算法思路,设计了一种新型的AVRTL算法,通过预处理函数、调整函数等,利用循环迭代寻优的方式得到有限点内所有双圈图的邻点可约全标号结果.对实验结果进行分析,发现几类图的标号规律,总结得到若干定理并给出证明,最后给出猜想:所有的双圈图均为AVRTL图.
基金supported by National Natural Science Foundation of China (Grant No.10871204)the Fundamental Research Funds for the Central Universities (Grant No.09CX04003A)
文摘In this paper,we determine graphs with the largest Laplacian spectral radius among the unicyclic and the bicyclic graphs on n vertices with k pendant vertices,respectively.
基金Supported by the National Natural Science Foundation of China (Grant No.10601001)the Natural Science Foundation of Anhui Province (Grant No.070412065)+3 种基金Project of Anhui Province for Young Teachers Research Supportin Universities (Grant No.2008jql083)Natural Science Foundation of Department of Education of Anhui Province(Grant No.2005kj005zd)Project of Anhui University on Leading Researchers ConstructionFoundation of Innovation Team on Basic Mathematics of Anhui University
文摘The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In our recent work, we have determined the graphs with maximal Laplacian spreads among all trees of fixed order and among all unicyclic graphs of fixed order, respectively. In this paper, we continue the work on Laplacian spread of graphs, and prove that there exist exactly two bicyclic graphs with maximal Laplacian spread among all bicyclic graphs of fixed order, which are obtained from a star by adding two incident edges and by adding two nonincident edges between the pendant vertices of the star, respectively.
基金Supported by the National Natural Science Foundation of China(No.11101057)China Postdoctoral Science Foundation(No.20110491443)+1 种基金the NSF of Education Ministry of Anhui province(No.KJ2012Z283)Scientific Research Foundation of Chuzhou University(No.2011kj004B)
文摘The spectral spread of a graph is defined to be the difference between the largest and the least eigenvalue of the adjacency matrix of the graph. A graph G is said to be bicyclic, if G is connected and ｜E（G）｜ = ｜V （G）｜ ＋ 1. Let B（n, g） be the set of bicyclic graphs on n vertices with girth g. In this paper some properties about the least eigenvalues of graphs are given, by which the unique graph with maximal spectral spread in B（n, g） is determined.
基金NSFC(Grant No.11761070,61662079)Postgraduate Innovation Project of Xinjiang,Xinjiang Normal University Undergraduate teaching project(SDJG2017-3)The Opening Project of Key Laboratory of Xinjiang Normal University(No:XJNUSYS082017A02).
文摘A graph G is nonsingular if its adjacency matrix A(G)is nonsingular.A nonsingular graph G is said to have an inverse G+if A(G)-1 is signature similar to a nonnegative matrix.Let H be the class of connected bipartite graphs with unique perfect matchings.We present a characterization of bicyclic graphs in H which possess unicyclic or bicyclic inverses.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Research on graph theory problems of topological parameters based on graph matrix spectrum”(2021D01C069)the National Natural Science Foundation of the People’s Republic of China“Research on spectral properties and related issue of graph operations”(12161085)。
