Geodesic
Counting Relations for General Zagreb Indices
Kragujevac Journal of Mathematics, Tome 38 (2014) no. 1, p. 95

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The first and second general Zagreb indices of a graph $G$, with vertex set $V$ and edge set $E$, are defined as $M_1^k = \sum_{v \in V} d(u)^k$ and $M_2^k = \sum_{uv \in E} [d(u), d(v)]^k$, where $d(v)$ is the degree of the vertex $v$ of $G$. We present combinatorial identities, relating $M_1^k$ and $M_2^k$ with counts of various subgraphs contained in the graph $G$.
Classification : 05C07 05C90
Keywords: Degree (of vertex), Zagreb index, General Zagreb index 
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     author = {G. Britto Antony Xavier and E. Suresh and I. Gutman},
     title = {Counting {Relations} for {General} {Zagreb} {Indices}},
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G. Britto Antony Xavier; E. Suresh; I. Gutman. Counting Relations for General Zagreb Indices. Kragujevac Journal of Mathematics, Tome 38 (2014) no. 1, p. 95 . http://geodesic.mathdoc.fr/item/KJM_2014_38_1_a6/