IJPAM: Volume 117, No. 1 (2017)

Title

THE FIRST ECCENTRIC ZAGREB INDEX OF THE $N^{TH}$
GROWTH OF NANOSTAR DENDRIMER $D_{3}[N]$

Authors

Zeinab Foruzanfar$^1$, Mohammad Reza Farahani$^2$,
Abdul Qudair Baig$^3$, Wasim Sajjad$^4$
$^1$Department of Engineering Sciences and Physics
Buein Zahra Technical University
Buein Zahra, Qazvin, IRAN
$^2$Department of Applied Mathematics
Iran University of Science and Technology (IUST)
Narmak, Tehran, 16844, IRAN
$^3$Department of Mathematics
COMSATS Institute of Information Technology
Attock Campus, PAKISTAN
$^4$Department of Mathematics
University of Sargodha
Mandi Bahauddin Campus
Mandi Bahauddin, PAKISTAN

Abstract

Let $G=(V,E)$ be a graph, where $V(G)$ is a non-empty set of vertices and $E(G)$ is a set of edges, $e=uv \in E(G)$, $d_{u}$ be degree of vertex $u$. The distance between two vertices of $G$ is the length of a shortest path connecting these two vertices. The eccentricity $\epsilon_u$ of a vertex $u$ in $G$ is the largest distance between $u$ and any other vertex of $G$. In this paper, we consider an infinite family of Nanostar Dendrimers and compute its First Eccentric Zagreb index. The First Eccentric Zagreb index was introduced by Ghorbani and Hosseinzadeh as $Zg_{1}^{*}(G)=\sum_{uv \in E(G)}\big(\epsilon_u+\epsilon_v\big)$, that $\epsilon_u$ is the eccentricity of a vertex $u$ and $\epsilon_v$ is the eccentricity of a vertex $v$ of $G$.

History

Received: 2017-07-22
Revised: 2017-10-28
Published: November 29, 2017

AMS Classification, Key Words

AMS Subject Classification: 05C90, 05C35, 05C12
Key Words and Phrases: molecular graph, Zagreb topological index, nanostar dendrimer, $D_{3}[n]$

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How to Cite?

DOI: 10.12732/ijpam.v117i1.10 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: 2017
Volume: 117
Issue: 1
Pages: 99 - 106


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