06093202

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06093202 Darafsheh, M.R. Khalifeh, M.H. Calculation of the Wiener, Szeged, and PI indices of a certain nanostar dendrimer. Ars Comb. 100, 289-298 (2011). 2011 Charles Babbage Research Centre, Winnipeg, MB EN dendrimer nanostar topological index Wiener index Szeged index PI-index Summary: Let $G=(V,E)$ be a simple connected graph with vertex set $V$ and edge set $E$. The Wiener index of $G$ is defined by $W(G)=\sum _{\{x,y\}\subseteq V}d(x,y)$, where $d(x,y)$ is the length of the shortest path from $x$ to $y$. The Szeged index of $G$ is defined by $Sz(G)=\sum _{e=uv\in E} n_{u}(e\mid G)n_{v}(e\mid G)$, where $n_{u}(e\mid G)$ (resp. $n_{v}(e\mid G)$) is the number of vertices of $G$ closer to $u$ (resp. $v$) than $u$ (resp. $u$). The Padmakar-Ivan index of $G$ is defined by $PI(G)=\sum _{e=uv\in E}[n_{eu}(e\mid G)+n_{ev}(e\mid G)]$, where $n_{eu}(e\mid G)$ (resp.$n_{ev}(e\mid G)$) is the number of edges of $G$ closer to $u$ (resp. $v$) than $v$ (resp. $u$). In this paper we will consider the graph of a certain nanostar dendrimer consisting of a chain of hexagons and find its topological indices such as the Wiener, Szeged and PI index.