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
Edge domatic numbers of complete n- partite graphs
β Scribed by Shiow-Fen Hwang; Gerard J. Chang
- Publisher
- Springer Japan
- Year
- 1994
- Tongue
- English
- Weight
- 575 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
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A Roman dominating function on a graph G is a labeling f : V (G) -β {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. A set { f 1 , f 2 , . . . , f d } of Roman dominating functions on G with the property that called a Roman dominating family (of functions) on G. The maximu
## Abstract Rosenfeld (1971) proved that the Total Colouring Conjecture holds for balanced complete __r__βpartite graphs. Bermond (1974) determined the exact total chromatic number of every balanced complete __r__βpartite graph. Rosenfeld's result had been generalized recently to complete __r__βpar
A graph G is m-partite if its points can be partitioned into m subsets Yl, . . . . Vm such that every line joins a point in Vi with a point in Vi, i + j. A complete m-partite graph contains every line joining Vi with V-. A complete graph Kp has every pair of its p points adjacent. The nth interchang