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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Suresh Elumalai
Department of Mathematics, Velammal Engineering College, Surapet, Chennai-66, Tamil Nadu, India
Electrical & Electronics Engineering

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New bounds on the hyper-Zagreb index for the simple connected graphs Suresh Elumalai; Toufik Mansour; Mohammad Ali Rostami
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.1.12

Abstract

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.
Co-Authors Mohammad Ali Rostami Toufik Mansour