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

Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami

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.


Keywords


hyper-Zagreb index, Zagreb indices, forgotten index

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DOI: http://dx.doi.org/10.5614/ejgta.2018.6.1.12

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ISSN: 2338-2287

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