Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 5 1 2020 06 01 On the edge geodetic and edge geodetic domination numbers of a graph 41 54 13946 10.22049/cco.2019.26347.1099 EN Vladimir Samodivkin University of Architecture, Civil Еngineering and Geodesy; Department of Mathematics Journal Article 2018 09 27 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. https://comb-opt.azaruniv.ac.ir/article_13946_a04e695bc31f9c7d591a19cbb7f8733e.pdf