On the edge geodetic and edge geodetic domination numbers of a graph

Abstract

In this paper, we study both concepts of geodetic dominating and edge geodetic dominating sets and derive some tight upper bounds on the edge geodetic and the edge geodetic domination numbers. We also obtain attainable upper bounds on the maximum number of elements in a partition of a vertex set of a connected graph into geodetic sets, edge geodetic sets, geodetic dominating sets and edge geodetic dominating sets, respectively.

Keywords

• domination number
• (edge) geodetic number
• (edge) geodetic domination number