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.
Scopus Subject Areas
- Harmonic index