A dominatin# set for a graph G = (V, E) is a subset of vertices V' c\_ V such that for all v โข V-V' there exists some uโข V' for which {v,u} โขE. The domination number of G is the size of its smallest dominating set(s). For a given graph G with minimum size dominating set D, let mz(G, D) denote the nu
On edge domination numbers of graphs
โ Scribed by Baogen Xu
- Book ID
- 108113515
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 166 KB
- Volume
- 294
- Category
- Article
- ISSN
- 0012-365X
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The problem of determining the domination number of a graph is a well known NPhard problem, even when restricted to planar graphs. By adding a further restriction on the diameter of the graph, we prove that planar graphs with diameter two and three have bounded domination numbers. This implies that
Topp, J. and L. Volkmann, On graphs wi',h equal domination and independent domination number, Discrete Mathematics 96 (1991) 75-80. Allan and Laskar have shown that Kt.s-free graphs are graphs with equal domination and independent domination numbers. In this paper new classes of graphs with equal d