On extremal bipartite bicyclic graphs

被引:11
作者
Huang, Jing [1 ]
Li, Shuchao [1 ]
Zhao, Qin [2 ]
机构
[1] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China
[2] Hubei Univ, Fac Math & Stat, Wuhan 430062, Peoples R China
基金
中国国家自然科学基金;
关键词
Estrada index; Kirchhoff index; Bipartite bicyclic graph; Complement graph; Closed walk; ESTRADA INDEX; KIRCHHOFF INDEX; RESISTANCE DISTANCES; FOLDING DEGREE; WIENER; TREES; PROTEINS; NUMBER; ENERGY;
D O I
10.1016/j.jmaa.2015.12.052
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let B-n(+) be the set of all connected bipartite bicyclic graphs with n vertices. The Estrada index of a graph G is defined as EE(G) = Sigma(n)(i=1) e(lambda i), where lambda(1), lambda(2,) ... , lambda(n) are the eigemralues of the adjacency matrix of G, and the Kirchhoff index of a graph G is defined as Kf (G) = Sigma(i<j) rij, where rij is the resistance distance between vertices vi and vj in G. The complement of G. is denoted by <(G)over bar>. In this paper, sharp upper bound on EE(G) (resp. Kf ((G) over bar)) of graph G in B-n(+) is established. The corresponding extremal graphs are determined, respectively. Furthermore, by means of some newly created inequalities, the graph G in B-n(+) with the second maximal EE(G) (rasp. Kf((G) over bar)) is identified as well. It is interesting to see that the first two bicyclic graphs in B-n(+) according to these two orderings are mainly coincident. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码:1242 / 1255
页数:14
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