A sequence of vertices in a graph G is called a legal dominating sequence if every vertex in the sequence dominates at least one vertex not dominated by those vertices that precede it, and at the end all vertices of G are dominated. While the length of a shortest such sequence is the domination number of G, in this paper we investigate legal dominating sequences of maximum length, which we call...

In this paper, we study both concepts of geodetic dominatingand edge geodetic dominating sets and derive some tight upper bounds onthe edge geodetic and the edge geodetic domination numbers. We also obtainattainable upper bounds on the maximum number of elements in a partitionof a vertex set of a connected graph into geodetic sets, edge geodetic sets,geodetic domin...

The power dominating set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes S that power dominates all the nodes, where a node v is power dominated if (1) v is in S or v has a neighbor in S, or (2) v has a neighbor w such that w and all of its neighbors except v are power dominated. We show a hardness of approximation threshold o...

Consider a graph G = (V, E) and a vertex subset A ⊆ V . A vertex v is positive-influence dominated by A if either v is in A or at least half the number of neighbors of v belong to A. For a target vertex subset S ⊆ V , a vertex subset A is a positive-influence target-dominating set for target set S if every vertex in S is positive-influence dominated by A. Given a graph G and a target vertex sub...

In this paper, we consider counting the number of ways to place kings on an k × n chessboard, such that every square is dominated by a king. Let f(k, n) be the number of dominating configurations. We consider the asymptotic behavior of the function f(k, n).

In ad hoc mobile wireless networks due to host mobility broadcasting is expected to be more frequently used to nd a route to a particular host to page a host and alarm all hosts A straight forward broadcasting by ooding is usually very costly and will result in substantial redundancy and more energy consumption Power consumption is an important issue since most mobile hosts operate on battery B...

In individual choices between alternatives x and y, the availability of a third alternative z, judged inferior to x but not to y, tends to increase preferences for x. Two experiments investigated corresponding strategic asymmetric dominance effects in games. In Experiment 1, 72 players chose strategies in six symmetric 3 · 3 games, each having one strategy dominating just one other, or in reduc...

In this research, we establish some new fixed-point results for a symmetric coupled dominated fuzzy mapping satisfying advanced contraction on closed ball in the setting of complete metric spaces. addition, notion hybrid fuzzy-graph-dominated mappings introduced spaces achieves problems. Some definitions and illustrative examples are given to validate our findings. Lastly, demonstrate originali...

In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a matching dimension to the game. This game is played on a graph $G$ by two players, named Dominator and Pairer. They alternately take turns choosing vertices of $G$ such that each vertex chosen by Domin...