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Farahani, Mohammad Reza, Baig, Abdul Qudair, Sajjad, Wasim. (1400). The second eccentric Zagreb index of the $n^{th}$ growth nanostar dendrimer $D_{3}[n]$. فناوری آموزش, 7(1), 23-28. doi: 10.22061/jdma.2022.1934
Mohammad Reza Farahani; Abdul Qudair Baig; Wasim Sajjad. "The second eccentric Zagreb index of the $n^{th}$ growth nanostar dendrimer $D_{3}[n]$". فناوری آموزش, 7, 1, 1400, 23-28. doi: 10.22061/jdma.2022.1934
Farahani, Mohammad Reza, Baig, Abdul Qudair, Sajjad, Wasim. (1400). 'The second eccentric Zagreb index of the $n^{th}$ growth nanostar dendrimer $D_{3}[n]$', فناوری آموزش, 7(1), pp. 23-28. doi: 10.22061/jdma.2022.1934
Farahani, Mohammad Reza, Baig, Abdul Qudair, Sajjad, Wasim. The second eccentric Zagreb index of the $n^{th}$ growth nanostar dendrimer $D_{3}[n]$. فناوری آموزش, 1400; 7(1): 23-28. doi: 10.22061/jdma.2022.1934

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

Journal of Discrete Mathematics and Its Applications
مقاله 3، دوره 7، شماره 1، فروردین 2022، صفحه 23-28    اصل مقاله (299.33 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22061/jdma.2022.1934
نویسندگان
Mohammad Reza Farahani* 1؛ Abdul Qudair Baig2؛ Wasim Sajjad3
1Department of Applied Mathematics, Iran University of Science and Technology (IUST),Narmak,Tehran 16844,Iran.
2Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Pakistan
3Department of Mathematics, University of Sargodha, Mandi Bahauddin Campus, Mandi Bahauddin Pakistan
تاریخ دریافت: 18 بهمن 1400،  تاریخ بازنگری: 25 بهمن 1400،  تاریخ پذیرش: 14 اسفند 1400 
چکیده
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 $G$.
کلیدواژه‌ها
Eccentricity؛ Zagreb Topological Index؛ Nanostar Dendrimer؛ D_{3}[n]
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