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

Document Type : Original paper


University of Architecture, Civil Đ•ngineering and Geodesy; Department of Mathematics


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.


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