A short note on hyper Zagreb index.

Abstract

In this paper, we present and analyze the upper and lower bounds on the Hyper-Zagreb index chi^2(G) of graph G in terms of the number of vertices (n), number of edges (m), maximum degree (Delta), minimum degree (delta) and the inverse degree (ID(G)). In addition, a counter example on the upper bound of the second Zagreb index for Theorems 2.2 and 2.4 from Ranjini et al. [Bol. Soc. Paran. Mat. (2013), 31, 51-55] is provided. Finally, we present the lower and upper bounds on chi^2(G)+chi^2(overline G), where overline G denotes the complement of G.