The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “The k -domatic number of a graph”

Signed total domination number of a graph

Bohdan Zelinka (2001)

Czechoslovak Mathematical Journal

Similarity:

The signed total domination number of a graph is a certain variant of the domination number. If v is a vertex of a graph G , then N ( v ) is its oper neighbourhood, i.e. the set of all vertices adjacent to v in G . A mapping f : V ( G ) → { - 1 , 1 } , where V ( G ) is the vertex set of G , is called a signed total dominating function (STDF) on G , if ∑ x ∈ N ( v ) f ( x ) ≥ 1 for each v ∈ V ( G ) . The minimum of values ∑ x ∈ V ( G ) f ( x ) , taken over all STDF’s of G , is called the signed total domination number of G and denoted by γ s t ( G ) . A theorem stating lower bounds for γ s t ( G ) is...

On the minus domination number of graphs

Hailong Liu, Liang Sun (2004)

Czechoslovak Mathematical Journal

Similarity:

Let G = ( V , E ) be a simple graph. A 3 -valued function f V ( G ) → { - 1 , 0 , 1 } is said to be a minus dominating function if for every vertex v ∈ V , f ( N [ v ] ) = ∑ u ∈ N [ v ] f ( u ) ≥ 1 , where N [ v ] is the closed neighborhood of v . The weight of a minus dominating function f on G is f ( V ) = ∑ v ∈ V f ( v ) . The minus domination number of a graph G , denoted by γ - ( G ) , equals the minimum weight of a minus dominating function on G . In this paper, the following two results are obtained. (1) If G is a bipartite graph of order n , then γ - ( G ) ≥ 4 n + 1 - 1 - n . (2) For any negative integer k and any positive integer...

A note on the independent domination number of subset graph

Xue-Gang Chen, De-xiang Ma, Hua Ming Xing, Liang Sun (2005)

Czechoslovak Mathematical Journal

Similarity:

The independent domination number i ( G ) (independent number β ( G ) ) is the minimum (maximum) cardinality among all maximal independent sets of G . Haviland (1995) conjectured that any connected regular graph G of order n and degree δ ≤ 1 2 n satisfies i ( G ) ≤ ⌈ 2 n 3 δ ⌉ 1 2 δ . For 1 ≤ k ≤ l ≤ m , the subset graph S m ( k , l ) is the bipartite graph whose vertices are the k - and l -subsets of an m element ground set where two vertices are adjacent if and only if one subset is contained in the other. In this paper, we give a sharp upper bound for i ( S m ( k , l ) ) and...

Restrained domination in unicyclic graphs

Johannes H. Hattingh, Ernst J. Joubert, Marc Loizeaux, Andrew R. Plummer, Lucas van der Merwe (2009)

Discussiones Mathematicae Graph Theory

Similarity:

Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S. The restrained domination number of G, denoted by γ r ( G ) , is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then γ r ( U ) ≥ ⎡ n / 3 ⎤ , and provide a characterization of graphs achieving this bound.

Domination in partitioned graphs

Zsolt Tuza, Preben Dahl Vestergaard (2002)

Discussiones Mathematicae Graph Theory

Similarity:

Let V₁, V₂ be a partition of the vertex set in a graph G, and let γ i denote the least number of vertices needed in G to dominate V i . We prove that γ₁+γ₂ ≤ [4/5]|V(G)| for any graph without isolated vertices or edges, and that equality occurs precisely if G consists of disjoint 5-paths and edges between their centers. We also give upper and lower bounds on γ₁+γ₂ for graphs with minimum valency δ, and conjecture that γ₁+γ₂ ≤ [4/(δ+3)]|V(G)| for δ ≤ 5. As δ gets large, however, the largest...