A short note on hyper Zagreb index

Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami, Gnanadhass Britto Antony Xavier

Abstract


In this paper, we present and analyze the upper and lower bounds on the Hyper Zagreb index $\chi^2(G)$ of graph $G$ in terms of the number of vertices $(n)$, number of edges $(m)$, maximum degree $(\Delta)$, minimum degree $(\delta)$ and the inverse degree $(ID(G))$. In addition, we give a counter example on the upper bound  of the second Zagreb index for Theorems 2.2 and  2.4 from \cite{ranjini}. Finally, we present lower and upper bounds on $\chi^2(G)+\chi^2(\overline G)$, where $\overline G$ denotes the complement of $G$.

Keywords


Zagreb index; Second Zagreb index; Hyper Zagreb index

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DOI: http://dx.doi.org/10.5269/bspm.v37i2.29148



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ISSN 0037-8712 (print) and ISSN 2175-1188 (on-line)

 

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