Beyond the Zagreb indices

Abstract

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.

Remarks on general zeroth-order Randić and general sum-connectivity indices

“…Remark 2. The inequality (9) was proven in [4] (see also [12,18]), the inequality (10) in [7,15,19,34], the inequality (11) in [14], and (12) in [23].…”

“…In addition to the aforementioned first Zagreb index M 1 (G) = 0 R 2 (G), in this paper we are interested in the following special cases of invariant 0 R α (G): m M 1 (G) = 0 R −2 (G) (the modified first Zagreb index [28]), ID(G) = 0 R −1 (G) (the inverse degree or modified total adjacency index [5] and [28] [8]). More on these topological indices can be found in [1,3,10,17,20] and in the references cited therein.…”

On Alberson irregularity measure of graphs

“…Recently, it was re-considered in [12] and named the forgotten index. Nowadays, there exist hundreds of papers on Zagreb indices and related matter [24,20,5,3,17].…”

On Extended Adjacency Index with Respect to Acyclic, Unicyclic and Bicyclic Graphs

“…Among all topological indices one of the most investigated are the degree based topological indices, among them, the old and widely studied topological index is Randić index [1], see the recent articles [2,3] and references cited there in. Recently researchers are studying various degree based topological indices such as Zagreb group indices [4][5][6][7][8][9], forgotten index [10][11][12][13], etc.…”