For a graph G=(V,E), subset D of vertex set V, is dominating G if every not in adjacent to at least one D. A with no isolated vertices called paired (PD-set), the subgraph induced by has perfect matching. The Min-PD problem requires compute PD-set minimum cardinality. decision version NP-complete even when belongs restricted classes such as bipartite graphs, chordal graphs etc. On other side, e...

The Fibonacci cube Γn is the subgraph of the n-dimensional cube Qn induced by the vertices that contain no two consecutive 1s. Using integer linear programming, exact values are obtained for γt(Γn), n ≤ 12. Consequently, γt(Γn) ≤ 2Fn−10 + 21Fn−8 holds for n ≥ 11, where Fn are the Fibonacci numbers. It is proved that if n ≥ 9, then γt(Γn) ≥ d(Fn+2 − 11)/(n− 3)e−1. Using integer linear programmin...

The domination game is played on a graph G by Dominator and Staller. The two players are taking turns choosing a vertex from G such that at least one previously undominated vertex becomes dominated; the game ends when no move is possible. The game is called D-game when Dominator starts it, and S-game otherwise. Dominator wants to finish the game as fast as possible, while Staller wants to prolo...

‎A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$‎. ‎The total domination number of a graph $G$‎, ‎denoted by $gamma_t(G)$‎, ‎is~the minimum cardinality of a total dominating set of $G$‎. ‎Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004)‎, ‎6...

In this paper we present an overview of a variety of efforts to attain good performance of Game AI for Domination games. These are a very popular kind of game sub-genre in which teams compete for control of locations. Due to the rules of the games, good performance is mostly dependant on overall strategy rather than the skill of individual team members.