Transmission and Reciprocal Transmission Based Topological Co-Indices of Graphs

Ramane H. S., Talwar S. Y., CANGÜL İ. N.

European Journal of Pure and Applied Mathematics, vol.13, no.5, pp.1057-1071, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.29020/nybg.ejpam.v13i5.3724
  • Journal Name: European Journal of Pure and Applied Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.1057-1071
  • Keywords: Transmission of a vertex, reciprocal transmission of a vertex, topological index, graph distance, 1ST ZAGREB INDEX
  • Bursa Uludag University Affiliated: Yes

Abstract

The transmission of a vertex u in a connected graph G is defined as the sum of the distances between u and all other vertices of a graph G. The reciprocal transmission of a vertex u in a connected graph G is defined as the sum of the reciprocal of distances between u and all other vertices of a graph G. In this paper, we introduce and study new topological co-indices based on the transmission and reciprocal transmission of a vertex, such as transmission and reciprocal transmission sum-connectivity co-indices, transmission and reciprocal transmission atom bond connectivity co-indices, transmission and reciprocal transmission geometric-arithmetic coindices, transmission and reciprocal transmission augmented Zagreb co-indices, and transmission and reciprocal transmission arithmetic-geometric co-indices. Further we obtain general formulae for some graphs.