A Class of Unicyclic Graphs With the Extremal Kirchhoff Index

Shubo Chen, Xia Cai, Ting Zeng, Lihui Yang

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

Abstract: The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices of the graph G, where 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. In this paper, we shall determine a class unicyclic graph with extremal Kirchhoff index.

Keywords: Resistance distance; Kirchhoff index; Unicyclic graph