On difference of Zagreb indices

Abstract The classical first and second Zagreb indices of a graph G are defined as M 1 = ∑ v d v 2 and M 2 = ∑ u v d u d v , where d v is the degree of the vertex v of G . So far, the difference of M 1 and M 2 has not been studied. We show that this difference is closely related to the vertex-degree-based invariant R M 2 = ∑ u v ( d u − 1 ) ( d v − 1 ) , and determine a few basic properties of R M 2 .

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