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

Suresh Elumalai (Department of Mathematics, Velammal Engineering College, Surapet, Chennai-66, Tamil Nadu, India)
Toufik Mansour (Department of Mathematics, University of Haifa, 3498838 Haifa, Israel)
Mohammad Ali Rostami (Institute for Computer Science, Friedrich Schiller University Jena, Germany)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications

The hyper-Zagreb index of a simple connected graph G is defined by χ2(G) = ∑uv ∈ E(G)(d(u) + d(v))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 Δ, and minimum vertex degree δ, first Zagreb index M1(G), second Zagreb index M2(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.