Complementary edge domination in graphs (Q1369009)

A subset \(F\) of the edge set \(E\) of a graph \(G\) is called an edge dominating set, if each edge of \(E-F\) has a common end vertex with an edge of \(F\). If there exists an edge dominating set \(F'\subseteq E-F\), where \(F\) is an edge dominating set, then \(F'\) is called a complementary edge dominating set. The minimum number of edges of a complementary dominating set in \(G\) is the complementary edge domination number \(\gamma_c'(G)\) of \(G\). In the paper, this numerical invariant of a graph is compared with others, namely with the edge domination number, with the edge independence number and with the maximum degree. Exact values of \(\gamma_c'(G)\) are found for complete graphs, complete bipartite graphs, circuits, paths, and wheels. At the end, results of the Nordhaus-Gaddum type are presented.