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

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

Displaying similar documents to “Restrained domination in unicyclic graphs”

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...

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...

Distance in stratified graphs

Gary Chartrand, Lisa Hansen, Reza Rashidi, Naveed Sherwani (2000)

Czechoslovak Mathematical Journal

Similarity:

A graph G is stratified if its vertex set is partitioned into classes, called strata. If there are k strata, then G is k -stratified. These graphs were introduced to study problems in VLSI design. The strata in a stratified graph are also referred to as color classes. For a color X in a stratified graph G , the X -eccentricity e X ( v ) of a vertex v of G is the distance between v and an X -colored vertex furthest from v . The minimum X -eccentricity among the vertices of G is the X -radius r a d X G of G ...

A note on periodicity of the 2-distance operator

Bohdan Zelinka (2000)

Discussiones Mathematicae Graph Theory

Similarity:

The paper solves one problem by E. Prisner concerning the 2-distance operator T₂. This is an operator on the class C f of all finite undirected graphs. If G is a graph from C f , then T₂(G) is the graph with the same vertex set as G in which two vertices are adjacent if and only if their distance in G is 2. E. Prisner asks whether the periodicity ≥ 3 is possible for T₂. In this paper an affirmative answer is given. A result concerning the periodicity 2 is added.

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...