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 $G$.
@article{29148,
title = {A short note on hyper Zagreb index},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {37},
year = {2017},
doi = {10.5269/bspm.v37i2.29148},
language = {EN},
url = {http://dml.mathdoc.fr/item/29148}
}
Elumalai, Suresh; Mansour, Toufik; Rostami, Mohammad Ali; Xavier, Gnanadhass Britto Antony. A short note on hyper Zagreb index. Boletim da Sociedade Paranaense de Matemática, Tome 37 (2017) . doi : 10.5269/bspm.v37i2.29148. http://gdmltest.u-ga.fr/item/29148/