An edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D. An edge domatic partition of a graph C=(V, E) is a collection of pairwise-disjoint edge dominating sets of G whose union is E. The maximum size of an edge domatic partition of G is call
Efficient edge domination problems in graphs
โ Scribed by Dana L. Grinstead; Peter J. Slater; Naveed A. Sherwani; Nancy D. Holmes
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 558 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
This paper generalizes dominating and efficient dominating sets of a graph. Let G be a graph with vertex set V(G). If f: V(G) ~ Y, where Y is a subset of the reals, the weight off is the sum of f(v) over all ve V(G). If the closed neighborhood sum off(v) at every vertex is at least 1, thenfis called
Sumner and Blitch defined a graph G to be k-y-critical if 7(G) = k and 7(G + uv) = k -1 for each pair u, v of nonadjacent vertices of G. We define a graph to be k-( 7,d)-critical if 7(G) = k and 7(G + uv) = k -I for each pair u, v of nonadjacent vertices of G that are at distance at most d apart. Th
In this paper, we consider r-dominating cliques in homogeneously orderable graphs (a common generalization of dually chordal and distance-hereditary graphs) and their relation to strict r-packing sets. We prove that a homogeneously orderable graph G possesses an r-dominating clique if and only if fo