An asteroidal triple is a set of three independent vertices such that between any two of them there exists a path that avoids the neighl.)ourhood of the third. Graphs that do not. co~,tain an asteroidal triple are called asteroidal triple-free (AT-free) graphs. AT-free graphs strictly contain the well-known class of cocomparability graphs, and are not necessarily perfect.. We present efficient,...

Recently, Bacsó and Tuza gave a full characterization of the graphs for which every connected induced subgraph has a connected dominating subgraph satisfying an arbitrary prescribed hereditary property. Using their result, we derive a similar characterization of the graphs for which any isolate-free induced subgraph has a total dominating subgraph that satisfies a prescribed additive hereditary...

Let G be a connected graph with vertex set V (G). A set S of vertices in G is called a weakly connected dominating set of G if (i) S is a dominating set of G and (ii) the graph obtained from G by removing all edges joining two vertices in V (G) \ S is connected. A weakly connected dominating set S of G is said to be minimum or a γw-set if |S| is minimum among all weakly connected dominating set...

A vertex subset S in a graph G is a dominating set if every vertex not contained in S has a neighbor in S. A dominating set S is a connected dominating set if the subgraph G[S] induced by S is connected. A connected dominating set S is a minimal connected dominating set if no proper subset of S is also a connected dominating set. We prove that there exists a constant ǫ > 10 such that every grap...

This paper addresses the scatternet formation for large scale multi-hop Bluetooth networks. We first describe an efficient method to build a Connected Dominating Set (CDS) as the backbone of multi-hop Bluetooth network, then propose new algorithms to form the dBBlue scatternets (Song et al., 2005) in each cluster. The final scatternet, M-dBBlue, guarantees the connectivity. Our experiment shows...

An edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D. An edge domatic partition of a graph C=(V, E) is a collection of pairwise-disjoint edge dominating sets of G whose union is E. The maximum size of an edge domatic partition of G is called the edge domatic number. In this paper, we study the edge domatic number of the complete parti...

Abstract. We propose a notion of extended dominating set whereby each node in an ad hoc network is covered by either a dominating neighbor or several 2-hop dominating neighbors. This work is motivated by cooperative communication in ad hoc networks where transmitting independent copies of a packet generates diversity and combats the effects of fading. In this paper we propose several efficient ...

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering, edge domination, and matching parameters is explored. In addition, the total vertex cover number is compared to the total domination number of ...

Abstract. The middle edge dominating graph Med(G) of a graph G=(V,E) is a graph with the vertex set E ∪S where S is the set of all minimal edge dominating set G and with two vertices u, v є E ∪S adjacent if u є E and V=F is a minimal edge dominating set of G containing u or u,v are not disjoint minimal edge dominating sets in S .In this paper we discuss about the middle edge dominating graph of...