THE UPPER EDGE TO EDGE DETOUR DOMINATION NUMBER OF A GRAPH (International Journal of Food and Nutritional Sciences, 2022)
An edge-to-edge detour dominating set ???? in a connected graph ???? is called a minimaledge-to-edge detour dominating set if no proper subset of ???? is an edge-to-edge detour dominating set of????. The upper edge-to-edge detour domination number ????????????????+ (????) of ???? is the maximum cardinality of aminimal edge-to-edge detour dominating set of ????. Some general properties satisfied by this concept arestudied. The upper edge-to-edge detour domination number of some standard graphs are determined. Itis shown that for any two positive integers ???? and ???? with 2 ≤ ???? ≤ ????, there exists a connected graph???? such that ????????????????(????) = ???? and ????????????????+ (????) = ????.