Lower and Upper Bounds for Hyper-Zagreb Index of Graphs

G. H.  SHIRDEL; H.  REZAPOUR; R.  NASIRI

doi:10.24996/ijs.2020.61.6.18

Authors

G. H. SHIRDEL Department of Mathematics, Faculty of Basic Sciences, University of Qom, Qom, Iran
H. REZAPOUR Department of Mathematics, Faculty of Basic Sciences, University of Qom, Qom, Iran
R. NASIRI Department of Mathematics, Faculty of Basic Sciences, University of Qom, Qom, Iran

DOI:

https://doi.org/10.24996/ijs.2020.61.6.18

Keywords:

Hyper-Zagreb index, Vertex degree, First and second Zagreb indices

Abstract

The topological indices are functions on the graph that do not depend on the labeling of their vertices. They are used by chemists for studying the properties of chemical compounds. Let be a simple connected graph. The Hyper-Zagreb index of the graph , is defined as ,where and are the degrees of vertex and , respectively. In this paper, we study the Hyper-Zagreb index and give upper and lower bounds for .