\((t,k)\)-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.