Extremal Kirchhoff Index of a Class of Unicyclic Graphs

Xia Cai, Ting Zeng, Lihui Yang, Jianguang Yang, Zhijun Guo, Shubo Chen

College of Science, Hunan City University, Yiyang, 413000, China

Abstract: The resistance distance between two vertices of a connected graph G is defined as the effective resistance between them in the corresponding electrical network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices of the graph G. In this paper, we shall characterize a class of unicyclic graph with the extremal Kirchhoff index.

Keywords: Resistance distance; Kirchhoff index; Unicyclic graph