A node in a graph G = (V,E) is said to dominate itself and all nodes adjacent to it. A set S C V is a dominating set for G if each node in V is dominated by some node in S and is a double dominating set for G if each node in V is dominated by at least two nodes in S. First we give a brief survey of
Inequalities relating domination parameters in cubic graphs
โ Scribed by Michael A. Henning; Peter J. Slater
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 787 KB
- Volume
- 158
- Category
- Article
- ISSN
- 0012-365X
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๐ SIMILAR VOLUMES
We study three recently introduced numerical invariants of graphs, namely, the signed domination number y., the minus domination number 7 and the majority domination number ymaj. An upper bound for ys and lower bounds for ;'-and Y,,~ are found, in terms of the order of the graph.
We consider the well-known upper bounds ยต(G) โค |V (G)|-โ(G), where โ(G) denotes the maximum degree of G and ยต(G) the irredundance, domination or independent domination numbers of G and give necessary and sufficient conditions for equality to hold in each case. We also describe specific classes of gr
A dominating set for a graph G = (V, E) is a subset of vertices V โ V such that for all v โ V -V there exists some u โ V for which {v, u} โ E. The domination number of G is the size of its smallest dominating set(s). We show that for almost all connected graphs with minimum degree at least 2 and q e