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 χ2(G) of graph G in terms of the number of vertices (n), number of edges (m), maximum degree (∆), minimum degree (δ) 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_ [20] is provided. Finally, we present the lower and upper bounds on χ2(G) + χ2(G), where G denotes the complement of G.