—In this paper, a Connected Dominating Set (CDS) construction algorithm CSCDS (Connected Subset based CDS) is proposed, which is based on the connected subset concept. The CSCDS contains two main stages, which are dominating set construction stage and connected dominating set construction stage respectively. In the first stage, the dominators are proposed based on the one hop white neighbor in...

A connected dominating set of a graph G = (V, E) is a subset of vertices CD ⊆ V such that every vertex not in CD is adjacent to at least one vertex in CD, and the subgraph induced by CD is connected. We show that, given an arc family F with endpoints sorted, a minimum-cardinality connected dominating set of the circular-arc graph constructed from F can be computed in O(|F |) time.

Article history: Received 14 November 2008 Received in revised form 15 January 2012 Accepted 27 February 2012 Available online xxxx

We continue the study, initiated in [3], of the complexity of deciding whether a given digraph D has a vertex-partition into two disjoint subdigraphs with given structural properties and given minimum cardinality. Let E be the following set of properties of digraphs: E ={strongly connected, connected, minimum out-degree at least 1, minimum in-degree at least 1, minimum semi-degree at least 1, m...

The aim of the present study is to follow topographical and morphological changes in the development of the amygdaloid basolateral complex (BLC) in the rabbit. The material consists of 35 brains of New Zealand rabbits of both sexes, divided into 7 age groups (P2-P90). In cresyl violet preparations BLC is already well visible on P2 and is composed of the lateral (divided into dorsolateral and ve...

Many authors studied cooperative games that arise from variants of dominating set games on graphs. In wireless networks, the connected dominating set is used to reduce routing table size and communication cost. In this paper, we introduce a connected dominating set game to model the cost allocation problem arising from a connected dominating set on a given graph and study its core. In addition,...

Let G = (V,E) be a graph and let S ⊆ V . A set of vertices in G totally dominates S if every vertex in S is adjacent to some vertex of that set. The least number of vertices needed in G to totally dominate S is denoted by γt(G,S). When S = V , γt(G,V ) is the well studied total domination number γt(G). We wish to maximize the sum γt(G) + γt(G,V1) + γt(G,V2) over all possible partitions V1, V2 o...