$(t,k)$-Geodetic Set of a Graph

Abstract

In this study we are going to give a new $(t,k)$-geodetic set definition. This is a refinement of the geodetic set definition given in $[11]$. With this new definition we obtain more information about the graph. We also give a relationship between the $(t,k)$-geodetic set and the integrity of a graph. By using a $(t,k)$-geodetic set we give a new proof for the upper bound of integrity of trees and unicycle graphs.