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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: Full Length 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] | ||
آمار تعداد مشاهده مقاله: 56 تعداد دریافت فایل اصل مقاله: 251 |