A pair of vertices of a graph is called a dominating pair if the vertex set of every path between these two vertices is a dominating set of the graph. A graph is a weak dominating pair graph if it has a dominating pair. Further, a graph is called a dominating pair graph if each of its connected induced subgraphs is a weak dominating pair graph. Dominating pair graphs form a class of graphs cont...

Let G = (V,E) be a connected graph. A connected dominating set S ⊂ V is a dominating set that induces a connected subgraph of G. The connected domination number of G, denoted γc(G), is the minimum cardinality of a connected dominating set. Alternatively, |V | − γc(G) is the maximum number of leaves in a spanning tree of G. Let δ denote the minimum degree of G. We prove that γc(G) ≤ |V | ln(δ+1)...

Given a graph, the minimum connected dominating set problem is to find a minimum cardinality subset of vertices D such that its induced subgraph is connected and each vertex outside D has at least one neighbor in D. Approximations of minimum connected dominating sets are often used to represent a virtual routing backbone in wireless networks. This paper proposes a constant-ratio approximation a...

-In wireless sensor network, virtual backbone formulation is a cost effective method to complete the broadcasting. Minimum connected dominating set is an outstanding candidate of virtual backbone. However, it is NP-Hard to find a minimum connected dominating set in an arbitrary graph. In this paper, we propose a novel backbone formation algorithm to construct a connected dominating set. In the ...

Connected dominating set is widely used in wireless ad-hoc and sensor networks as a routing and topology control backbone to improve the performance and increase the lifetime of the network. Most of the distributed algorithms for approximating connected dominating set are based on constructing maximal independent set. The performance of such algorithms highly depends on the relation between the...