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/