Transmission and Reciprocal Transmission Based Topological Co-Indices of Graphs

Harishchandra S. Ramane, Saroja Y. Talwar, Ismail Naci Cangul

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 co-indices, 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.

Keywords

transmission of a vertex; reciprocal transmission of a vertex; topological index; graph distance

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