The edge domination number of connected graphs.
Araya Chaemchan · 2010
A subset X of edges in a graph G is called an edge dominating set of G if every edge not in X is adjacent to some edge in X. The edge domination number γ ′(G) ofG is the minimum cardinality taken over all edge dominating sets of G. Let m, n and k be positive integers with n − 1 ≤ m ≤ () n, G(m, n) be the set of all non-isomorphic connected 2 graphs of order n and size m, and G(m, n; k) ={G ∈G(m, n):γ ′ (G) =k}. We are able to determine all integers m, n, k for which G(m, n; k) = ∅.