On The Harmonic Index and The Minimum Degree of A Graph
نویسندگان
چکیده
The harmonic index H(G) of a graph G is the sum of 2 d(u) + d(υ) over all edges uυ of G, where d(u) denotes the degree of a vertex u in G. In this paper, we give the minimum value of H(G) for graphs G with given minimum degree δ(G) ≥ 2 and characterize the corresponding extremal graph. Furthermore, we prove a best-possible lower bound on the harmonic index of a triangle-free graph G with arbitrary minimum degree δ(G).
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تاریخ انتشار 2013