We study the paired-domination problem on interval graphs and circular-arc graphs. Given an interval model with endpoints sorted, we give an O(m + n) time algorithm to solve the paired-domination problem on interval graphs. The result is extended to solve the paired-domination problem on circular-arc graphs in O(m(m+ n)) time. MSC: 05C69, 05C85, 68Q25, 68R10, 68W05

Let G = (V,E) be a graph without isolated vertices. A set S ⊆ V is a total dominating set if every vertex in V is adjacent to at least one vertex in S. A total dominating set S ⊆ V is a paired-dominating set if the induced subgraph G[S] has at least one perfect matching. The paired-domination number γpr(G) is the minimum cardinality of a paired-domination set of G. In this paper, we provide a c...

The game domination number is a graph invariant that arises from a game, which is related to graph domination in a similar way as the game chromatic number is related to graph coloring. In this paper we show that verifying whether the game domination number of a graph is bounded by a given integer is PSPACEcomplete. This contrasts the situation of the game coloring problem whose complexity is s...

In this paper, we study a generalization of the paired domination number. Let G= (V ,E) be a graph without an isolated vertex. A set D ⊆ V (G) is a k-distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The k-distance paired domination number p(G) is the cardinality of a smallest k-distance paired dominating set of G. ...

The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...

A paired-dominating set of a graph is a dominating set of vertices whose induced subgraph has a perfect matching, while the paired-domination number is the minimum cardinality of a paired-dominating set in the graph. Recently, Chen, Sun and Xing [Acta Mathematica Scientia Series A Chinese Edition 27(1) (2007), 166–170] proved that a cubic graph has paired-domination number at most three-fifths ...

The paired bondage number (total restrained bondage number, independent bondage number, k-rainbow bondage number) of a graph G, is the minimum number of edges whose removal from G results in a graph with larger paired domination number (respectively, total restrained domination number, independent domination number, k-rainbow domination number). In this paper we show that the decision problems ...

In this paper, we introduce a fractional domination game arising from fractional domination problems on graphs and focus on its balancedness and concavity. We first characterize the core of the fractional domination game and show that its core is always non-empty taking use of dual theory of linear programming. Furthermore we study concavity of this game.

Given a graph \(G=(V(G), E(G))\), the size of minimum dominating set, paired and total set G are denoted by \(\gamma (G)\), _{pr}(G)\), _{t}(G)\), respectively. For positive integer k, k-packing in is \(S \subseteq V(G)\) such that for every pair distinct vertices u v S, distance between at least \(k+1\). The number order largest \(\rho _{k}(G)\). It well known _{pr}(G) \le 2\gamma (G)\). In th...