On the topological matrix and topological indices

KAYA GÖK G.

AKCE International Journal of Graphs and Combinatorics, vol.17, no.1, pp.252-258, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1016/j.akcej.2019.07.001
  • Journal Name: AKCE International Journal of Graphs and Combinatorics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.252-258
  • Keywords: Bounds, Topological indices, Topological matrix
  • Hakkari University Affiliated: Yes

Abstract

The topological matrix (Formula presented.) of a graph (Formula presented.) are indexed by (Formula presented.). If (Formula presented.) then the (Formula presented.) of (Formula presented.) is 1 and the (Formula presented.) of (Formula presented.) is 0 for otherwise. In this paper, an upper bound for this topological matrix is found and the weighted topological matrix is defined. Also, some inequalities for the topological energy and the weighted Laplacian topological energy and of (Formula presented.) are obtained. The Topological index (Formula presented.) of a graph (Formula presented.) is qualified by (Formula presented.). Some relations are found for basic mathematical operations of (Formula presented.) and some bounds are reported for some topological indices in this paper.