New bounds on the hyper-Zagreb index for the simple connected graphs.

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Abstract

The hyperZagreb index of a simple connected graph G is defined by chi ^2(G) = sum_uv in E(G) left( d(u) + d(v) right)^2. In this paper, we establish, analyze and compare some new upper bounds on the HyperZagreb index in terms of the number of vertices n, number of edges m, maximum vertex degree Delta, and minimum vertex degree delta, first Zagreb index M_1(G), second Zagreb index M_2(G), harmonic index H(G), and inverse edge degree IED(G). In addition, we give the identities on HyperZagreb index and its coindex for the simple connected graphs.