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Graphs with convex domination number close to their order

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Cyman J., Lemańska M., Raczek J.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 2

307-316

For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance $d_G(u,v)$ between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length $d_G(u,v)$ is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number $γ_{con}(G)$ of a graph G is the minimum cardinality of a convex dominating set in G. Graphs with the convex domination number close to their order are studied. The convex domination number of a Cartesian product of graphs is also considered.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Cyman J.

1 Lemańska M.

1 Raczek J.

1 2006

Wyniki wyszukiwania

Graphs with convex domination number close to their order