ON HYPER ZAGREB INDEX OF CERTAIN
GENERALIZED GRAPH STRUCTURES
Zhen Wang1, Natarajan Chidambaram2
Selvaraj Balachandran3
1School of Computer Engineering
Anhui Wenda University of Information Engineering
Hefei - 230032, CHINA
2 Department of Mathematics
Srinivasa Ramanujan Centre
SASTRA Deemed University
Kumbakonam - 612 001, INDIA
3Department of Mathematics, School of Arts
Sciences and Humanities, SASTRA Deemed to be University
Thanjavur - 613 401, Tamilnadu, INDIA

Abstract

Let $G=(V,E)$ be a graph with $n$ vertices and $m$ edges. The hyper Zagreb index of $G$, denoted by $HM(G)$, is defined as

\begin{displaymath}HM(G) =\sum\limits_{uv \in E(G)}\left[d_{G}(u)+d_G(v)\right]^{2},\end{displaymath}

where $d_G(v)$ denotes the degree of a vertex $v$ in $G$. In this paper we compute the hyper Zagreb index of certain generalized graph structures such as generalized thorn graphs and generalized theta graphs. Also,for the first time, we determine exact values for hyper Zagreb index of some cycle related graphs, namely cycle with parallel $P_k$ chords, cycle with parallel $C_k$ chords and shell type graphs.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 6
Year: 2019

DOI: 10.12732/ijam.v32i6.8

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