For a graph G, the definitions of doknation number, denoted y(G), and independent domination number, denoted i(G), are given, and the following results are obtained: oorollrrg 1. For any graph G, y(L(G)) = i@(G)), where Z,(G) is the line graph of G. (This $xh!s t.lic rtsult ~(L(T))~i(L(T)), h w ere
On domination numbers of graph bundles
β Scribed by Blaz Zmazek; Janez Zerovnik
- Publisher
- Springer-Verlag
- Year
- 2006
- Tongue
- English
- Weight
- 265 KB
- Volume
- 22
- Category
- Article
- ISSN
- 1598-5865
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Graph bundles generalize the notion of covering graphs and products of graphs. The chromatic numbers of product bundles with respect to the Cartesian, strong and tensor product whose base and fiber are cycles are determined. ## 1. Introduction If G is a graph, V(G) and E(G) denote its vertex and e
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
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