Department of Mathematics
The harmonic index of a graph
Copyright ©2014 Rocky Mountain Mathematics Consortium The harmonic index of a graph G is defined as the sum of weights (Formula presented.) of all edges vi vj of G, where d(vi) denotes the degree of the vertex vi in G. In this paper, we study how the harmonic index behaves when the graph is under perturbations. These results are used to provide a simpler method for determining the unicyclic graphs with maximum and minimum harmonic index among all unicyclic graphs, respectively. Moreover, a lower bound for harmonic index is also obtained.
Bound, Effect, Graph, Harmonic index
Source Publication Title
Rocky Mountain Journal of Mathematics
Rocky Mountain Mathematics Consortium
Li, Jianxi, and Wai Chee Shiu. "The harmonic index of a graph." Rocky Mountain Journal of Mathematics 44.5 (2014): 1607-1620.