On difference of Zagreb indices


FURTULA B., GUTMAN I., Ediz S.

DISCRETE APPLIED MATHEMATICS, vol.178, pp.83-88, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 178
  • Publication Date: 2014
  • Doi Number: 10.1016/j.dam.2014.06.011
  • Journal Name: DISCRETE APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.83-88
  • Keywords: Degree (of vertex), Zagreb index, First Zagreb index, Second Zagreb index, SQUARES, SUM, IRREGULARITY
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

The classical first and second Zagreb indices of a graph G are defined as M-1 = Sigma(v) d(v)(2) and M-2 = Sigma(uv) 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 RM2 = Sigma(uv) (d(u) - 1) (d(v) - 1), and determine a few basic properties of RM2. (C) 2014 Elsevier B.V. All rights reserved.