The two Zagreb indices M 1 = ∑ v d(v) 2 and M 2 = ∑ uv d(u) d(v) are vertex-degree-based graph invariants that have been introduced in the 1970s and extensively studied ever since. In the last few years, a variety of modifications of M 1 and M 2 were put forward. The present survey of these modified Zagreb indices outlines their main mathematical properties, and provides an exhaustive bibliography.

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Let G be a simple connected graph with n vertices and m edges andi . We prove some new lower bounds for Kf (G) in terms of some of the parameters

Abstract. Let G be an undirected connected graph with n ; n 2, vertices and m edges with vertex degreesLower and upper bounds of a graph invariants, referred to as the first Zagreb index, and