IJPAM: Volume 105, No. 1 (2015)

THE TOPOLOGICAL INDICES OF
NON-COMMUTING GRAPH OF A FINITE GROUP

M. Jahandideh$^1$, N.H. Sarmin$^2$, S.M.S. Omer$^3$
$^1$Department of Mathematics
Shahid Chamran University of Ahvaz
Ahvaz, IRAN
$^2$Department of Mathematical Sciences
Faculty of Science
University Teknologi Malaysia
81310 UTM Johor Bahru, Johor, MALAYSIA
$^3$Department of Mathematics
Faculty of Science
University of Benghazi
Benghazi, LIBYA


Abstract. Assume $G$ is a non-abelian finite group. The non-commuting graph $\Gamma_G$ of $G$ is defined as a graph with vertex set $G-Z(G)$ in which $Z(G)$ is the center of $G$ and two distinct vertices $x$ and $y$ are joined if and only if $xy\not=yx$. Various topological indices have been determined for simple and connected graphs. Since non-commuting graph is a simple and connected graph, topological indices could be defined for it. The main objective of this article is to calculate various topological indices including the Szeged index, Edge-Wiener index, the first Zagreb index and the second Zagreb index for the non-commuting graph of $G$.

Received: June 26, 2015

AMS Subject Classification: 05C12

Key Words and Phrases: non-commuting graph, Szeged index, edge-wiener index, the first Zagreb index, the second Zagreb index

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DOI: 10.12732/ijpam.v105i1.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 1
Pages: 27 - 38


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