Learn More
A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. A set S of vertices in G is a total dominating set ofG if every vertex of G is adjacent to some vertex in S. The matching number is the maximum cardinality of a matching of G, while the total domination number of G is the minimum cardinality of a total(More)
4 A set S of vertices in a graph H = (V, E) with no isolated vertices is a paired-dominating 5 set of H if every vertex of H is adjacent to at least one vertex in S and if the subgraph 6 induced by S contains a perfect matching. Let G be a permutation graph and π be its 7 corresponding permutation. In this paper we present an O(mn) time algorithm for(More)
The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known domination problem in graphs. In 2002, Haynes et al. considered the graph theoretical representation of this problem as a variation of the domination problem. They defined a set S to be a power dominating(More)
For a graph G of order n, let (G), 2(G) and t(G) be the domination, double domination and total domination numbers of G, respectively. The minimum degree of the vertices of G is denoted by (G) and the maximum degree by (G). In this note we prove a conjecture due to Harary and Haynes saying that if a graph G has (G); ( 9 G)¿ 4, then 2(G) + 2( 9 G)6 n− (G) +(More)
A clique is defined as a complete subgraph maximal under inclusion and having at least two vertices. A k-clique-coloring of a graph G is an assignment of k colors to the vertices of G such that no clique of G is monochromatic. Bacsó et al. (SIAM J Discrete Math 17:361–376, 2004) noted that the clique-coloring number is unbounded even for the line graphs of(More)