New Bounds on the Hyper-Zagreb Index for the Simple Connected Graphs

Suresh Elumalai • Toufik Mansour • Mohammad Ali Rostami

Download full text
(English, 12 pages)

Abstract

The hyper-Zagreb 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 Hyper-Zagreb 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 Hyper-Zagreb index and its coindex for the simple connected graphs.

Metrics

  • 111 views
  • 73 downloads

Journal

Electronic Journal of Graph Theory and Applications

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to ... see more