Third Zagreb Index of Graphs with Added Edges

Mahalank P., CANGÜL İ. N.

Bulletin of Computational Applied Mathematics, vol.10, no.1, pp.81-92, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 1
  • Publication Date: 2022
  • Journal Name: Bulletin of Computational Applied Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.81-92
  • Keywords: Edge addition, Graph, Pendant edge, Third Zagreb index, Topological index, Vertex degree
  • Bursa Uludag University Affiliated: Yes


Edge deletion and addition to a graph is an important combinatorial method in Graph Theory which enables one to calculate some properties of a graph by means of similar and usually simpler graphs. In this paper, as a sequel to recent papers on edge deletion and addition, we consider the change in the third Zagreb index of a simple graph G when an arbitrary edge is added. The effect of adding any kind of edge to a graph is shown to be an integer congruent to 2 modulo 6. This result can be used to calculate the third Zagreb index of larger graphs in terms of the Zagreb indices of smaller graphs. As some examples, some inequalities for the change of Zagreb indices of path, cycle, star, complete, complete bipartite and tadpole graphs are given.