On Harmonic Index and Diameter of Unicyclic Graphs


The Harmonic index H(G) of a graph G is defined as the sum of the weights 2 d(u) + d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u in G. In this work, we prove the conjecture H(G) D(G) ≥ 1 2 + 1 3(n− 1) given by Jianxi Liu in 2013 when G is a unicyclic graph and give a better bound H(G) D(G) ≥ 1 2 + 2 3(n− 2) , where n is the order… (More)

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