Degree Kirchhoff Index of Bicyclic Graphs

作者:Tang, Zikai*; Deng, Hanyuan
来源:Canadian Mathematical Bulletin, 2017, 60(1): 197-205.
DOI:10.4153/CMB-2016-063-5

摘要

Let G be a connected graph with vertex set V (G). The degree Kirchhoff index of G is defined as S'(G) = Sigma{u,v}cv(G) d(u)d(v)R(u,v), where d(u) is the degree of vertex u, and R(u, v) denotes the resistance distance between vertices u and v. In this paper, we characterize the graphs having maximum and minimum degree Kirchhoff index among all n-vertex bicyclic graphs with exactly two cycles.