On the entire Zagreb indices of the line graph and line cut-vertex graph of the subdivision graph
Let \(G=(V,E)\) be a graph. Then the first and second entire Zagreb indices of \(G\) are defined, respectively, as \(M_{1}^{\varepsilon}(G)=\displaystyle \sum_{x \in V(G) \cup E(G)} (d_{G}(x))^{2}\) and \(M_{2}^{\varepsilon}(G)=\displaystyle \sum_{\{x,y\}\in B(G)} d_{G}(x)d_{G}(y)\), where \(B(G)\) denotes the set of all 2-element subsets \(\{x,y\}\) such that \(\{x,y\} \subseteq V(G) \cup E(G)\) and members of \(\{x,y\}\) are adjacent or incident to each other. In this paper, we obtain the entire Zagreb indices of the line graph and line cut-vertex graph of the subdivision graph of the friendship graph.
2015 ◽
Vol 91
(3)
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pp. 353-367
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2018 ◽
Vol 2(2018)
(1)
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pp. 66-73
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2019 ◽
Vol 20
(2)
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pp. 305-320
Keyword(s):
2012 ◽
Vol 1
(4)
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