We propose a memory efficient self-stabilizing protocol building k-independant dominating sets. A k-independant dominating set is a k-independant set and a k-dominating set. A set of nodes, I, is kindependent if the distance between any pair of nodes in I is at least k + 1. A set of nodes, D, is a k-dominating if every node is within distance k of a node of D. Our algorithm, named SID, is silen...

Let G be a graph with no isolated vertex and f : V ( ) → {0, 1, 2} function. i = { x ∈ } for every . We say that is total Roman dominating function on if in 0 adjacent to at least one 2 the subgraph induced by 1 ∪ has vertex. The weight of ω ∑ v minimum among all functions domination number , denoted γ t R It known general problem computing NP-hard. In this paper, we show H nontrivial graph, th...

Dominating sets in their many variations model a wealth of optimization problems like facility location or distributed le sharing. For instance, when a request can occur at any node in a graph and requires a server at that node, a minimumdominating set represents a minimum set of servers that serve an arbitrary single request by moving a server along at most one edge. This paper studies dominat...

We investigate a domination-like problem from the exact exponential algorithms viewpoint. The classical Dominating Set problem ranges among one of the most famous and studied NP -complete covering problems [6]. In particular, the trivial enumeration algorithm of runtime O∗(2n) 4 has been improved to O∗(1.4864n) in polynomial space, and O∗(1.4689n) with exponential space [9]. Many variants of th...

Definition of dominating function on a fractional graph G has been introduced. Fractional parameters such as domination number and upper defined. Domination with fuzzy Intuitionistic environment, have found by formulating Linear Programming Problem.

Let G be a graph of order n. For every v ∈ V (G), let EG(v) denote the set of all edges incident with v. A signed k-submatching of G is a function f : E(G) −→ {−1, 1}, satisfying f(EG(v)) ≤ 1 for at least k vertices, where f(S) = ∑ e∈S f(e), for each S ⊆ E(G). The maximum of the value of f(E(G)), taken over all signed k-submatching f of G, is called the signed k-submatching number and is denote...

In our previous paper on this topic, we introduced the notion of k-Hessian measure associated with a continuous k-convex function in a domain Ω in Euclidean n-space, k = 1, · · · , n, and proved a weak continuity result with respect to local uniform convergence. In this paper, we consider k-convex functions, not necessarily continuous, and prove the weak continuity of the associated k-Hessian m...

This article proposes a scenario-based algorithm for cluster formation and management in mobile ad hoc networks. Depending on the application a centralized or distributed algorithm based on (k, r) −Dominating Set is used for the selection of clusterheads and gateway nodes. Here k is the minimum number of clusterheads per node in the network and r is the maximum number of hops between the node a...