New lower bounds for the second variable Zagreb index Articles uri icon

publication date

  • July 2018

start page

  • 194

end page

  • 210

issue

  • 1

volume

  • 36

international standard serial number (ISSN)

  • 1382-6905

abstract

  • The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index , and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the RandiAc, the second Zagreb and the modified Zagreb indices.

keywords

  • Second variable Zagreb index; Graph invariant; Vertex-degree-based graph invariant; Topological index