The complete cototal domination set is said to be irredundant dominating if for each u ∈ S, NG [S − {u}] ≠ [S]. minimum cardinality taken over all an called number and denoted by γircc(G). Here a new parameter was introduced the study of bounds γircc(G) initiated.

Deep-inelastic diffractive scaling provides fundamental insight into the QCD pomeron. It is argued that single gluon domination of the structure function, together with the well-known Regge pole property, determines that the pomeron carries color-charge parity Cc = −1 and, at short distances, is in a super-critical phase of Reggeon Field Theory. The main purpose of the talk is to describe the r...

We propose a memory efficient self-stabilizing protocol building k-independent dominating sets. A k-independent dominating set is a k-independent set and a kdominating set. A set of nodes, I, is k-independent 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 k be a positive integer and G = (V,E) a connected graph of order n. A set D ⊆ V is called a distance k-dominating set of G if each x ∈ V (G)−D is within distance k from some vertex of D. The k-domination number of G, denoted by γk(G), is the minimum cardinality over all distance k-dominating sets. Determining γk(G) has a significant impact on an efficient design of routing protocols in netw...

A unit disk graph is the intersection graph of a set of unit diameter disks in the plane. In this paper we consider liar’s domination problem on unit disk graphs, a variant of dominating set problem. We call this problem as Euclidean liar’s domination problem. In the Euclidean liar’s domination problem, a set P = {p1, p2, . . . , pn} of n points (disk centers) are given in the Euclidean plane. ...

A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...