TITLE:
On the Harmonic Index of Triangle-Free Graphs
AUTHORS:
Jianxi Liu
KEYWORDS:
Harmonic Index; Minimum Degree; Triangle-Free
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.8,
August
6,
2013
ABSTRACT:
The harmonic index of a graphG is defined as where d(u) denotes the degree of a vertex u in G . In this work, we give another expression for the Harmonic index. Using this expression, we give the minimum value of the harmonic index for any triangle-free graphs with order n and minimum degree δ ≥ k for k≤ n/2 and show the corresponding extremal graph is the complete graph.