2020/11/10 by Abdolghafourian, A., Iranmanesh, Mohammad A.
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2011.05752
The harmonic index of a graph G, is defined as the sum of weights (2)/(d(u)+d(v)) of all edges uv of G, where d(u) is the degree of the vertex u in G. In this paper we find the minimum harmonic index of bicyclic graph of order n and diameter d. We also characterized all bicyclic graphs reaching the minimum bound.