Minimizing Kirchhoff index among graphs with a given vertex bipartiteness
Minimizing Kirchhoff index among graphs with a given vertex bipartiteness
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最小化具有给定顶点二分性的图之间的基尔霍夫指数
DOI：
10.1016/j.amc.2016.06.017
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发表时间：
2016-12-01
影响因子：
4
通讯作者：
Pan, Xiang-Feng
中科院分区：
文献类型：
--
作者：
Liu, Jia-Bao;Pan, Xiang-Feng
如果图G的每条边都被单位电阻所代替，则图G的任意两个顶点之间的电阻距离被定义为它们之间的有效电阻。Kirchhoff指数Kf（G）是G中所有顶点对之间的电阻距离之和。图G的点二分性v（B）是指从图G中删除使图G成为二分图的顶点的最小数目。本文刻画了在顶点数n固定且点偶性固定的图中，Kf（G）值最小的图，
The resistance distance between any two vertices of a graph G is defined as the effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff-index Kf(G) is the sum of the resistance distances between all the pairs of vertices in G. The vertex bipartiteness v(b) of a graph G is the minimum number of vertices whose deletion from G results in a bipartite graph. In this paper, we characterize the graph having the minimum Kf(G) values among graphs with a fixed number n of vertices and fixed vertex bipartiteness, 1