The extremal Kirchhoff index of a class ofunicyclic graphs

摘要

The Kirchhoff index K f (G) of a graph G is the sum of resistancedistances between all pairs of vertices. A fully loaded unicyclic graph isa unicyclic graph with the property that there is no vertex with degreeless than 3 in its unique cycle. In this paper, we determine the minimaland maximal Kirchhoff indices among all fully loaded unicyclic. graphswith n vertices, and characterize the extremal graphs.