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Search results for: PAIRED-DOMINATION NUMBER
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Lower bound on the paired domination number of a tree
PublicationW pracy przedstawione jest ograniczenie dolne dla liczby dominowania parami oraz scharakteryzowane są wszystkie drzewa ekstremalne.
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The paired-domination and the upper paired-domination numbers of graphs
PublicationIn this paper we obtain the upper bound for the upper paired-domination number and we determine the extremal graphs achieving this bound. Moreover we determine the upper paired- domination number for cycles.
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All graphs with paired-domination number two less than their order
PublicationLet G=(V,E) be a graph with no isolated vertices. A set S⊆V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number γp(G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199-206] Haynes and Slater...
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Distance paired domination numbers of graphs
PublicationW pracy przedstawione są pewne własności liczb k-dominowania parami w grafach. Wykazane jest, że problem decyzyjny liczby k-dominowania parami jest problemem NP-zupełnym nawet dla grafów dwudzielnych. Przedstawione są ograniczenia górne i dolne dla liczby k-dominowania parami w drzewach i scharakteryzowane drzewa, w których te ograniczenia są osiągnięte.
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Paired domination versus domination and packing number in graphs
PublicationGiven a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and...
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Block graphs with large paired domination multisubdivision number
PublicationThe paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
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Paired domination and doubly domination in graphs
PublicationW rozprawie poruszane są zagadnienia związane z dominowaniem parami w grafach oraz domiowaniem totalno - powściągniętym w grafach. Ponadto omawiane są zagadnienia związane ze złożonością obliczeniową różnych problemów dominowania w grafach.
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Total domination in versus paired-domination in regular graphs
PublicationA subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph induced by S contains a perfect matching, then S is a paired-dominating set. The domination number, denoted γ(G), is the minimum cardinality of a dominating set of G, while the...
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Paired domination subdivision and multisubdivision numbers of graphs
PublicationThe paired domination subdivision number sdpr(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the paired domination number of G. We prove that the decision problem of the paired domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the paired domination muttisubdivision number of a nonempty graph...
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On trees with double domination number equal to 2-domination number plus one
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...