The second eccentric Zagreb index of the $n^{th}$ growth nanostar dendrimer $D_{3}[n]$

Document Type : Original Article

Authors

1 Department of Applied Mathematics, Iran University of Science and Technology (IUST),Narmak,Tehran 16844,Iran.

2 Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Pakistan

3 Department of Mathematics, University of Sargodha, Mandi Bahauddin Campus, Mandi Bahauddin Pakistan

Abstract

Let $G=(V,E)$ be an ordered pair, where $V(G)$ is a non-empty set
of vertices and $E(G)$ is a set of edges called a graph. We denote
a vertex by $v$ where $v \in V(G)$ and edge by $e$ where $e=uv \in
E(G)$. we denote degree of vertex $v$ by $d_{v}$ which is defined
as the number of edges adjacent with vertex $v$. The distance
between two vertices of $G$ is the length of a shortest path
connecting these two vertices which is denoted by $d(u,v)$ where
$u,v \in V(G)$. The eccentricity $ecc(v)$ of a vertex $v$ in $G$
is the distance between vertex $v$ and vertex farthest from $v$ in
$G$. In this paper, we consider an infinite family of Nanostar
Dendrimers and compute its Second Eccentric Zagreb index.
M.Ghorbani and Hosseinzadeh introduced Second eccentric zagreb
index as $EM_{2}(G)=\sum_{uv \in E(G)}\big(ecc(u)\times
ecc(v)\big)$, that $ecc(u)$ denotes the eccentricity of a vertex
$u$ and $ecc(v)$ denotes the eccentricity of a vertex $v$ of $G$.

Graphical Abstract

The second eccentric Zagreb index of the $n^{th}$ growth nanostar dendrimer $D_{3}[n]$

Keywords

Journal of Discrete Mathematics and Its Applications
Volume 7, Issue 1
January 2022
Pages 23-28

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History

  • Receive Date: 07 February 2022
  • Revise Date: 14 February 2022
  • Accept Date: 05 March 2022
  • Publish Date: 10 March 2022

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