The ratio of the connected domination number, γc, and the domination number, γ, is strictly bounded from above by 3. It was shown by Zverovich that for every connected (P5, C5)-free graph, γc = γ. In this paper, we investigate the interdependence of γ and γc in the class of (Pk, Ck)-free graphs, for k ≥ 6. We prove that for every connected (P6, C6)-free graph, γc ≤ γ+1 holds, and there is a fam...

Connected Dominating Sets (CDSs) can serve as virtual backbones for wireless networks. A smaller virtual backbone (minimum size CDS) incurs less communication overhead. Unfortunately, computing a minimum size CDS is NP-hard and thus many algorithms were developed which concentrates on how to construct smaller CDSs. Aiming for minimum number of nodes in CDS, results in CDSs that are highly unsta...

This paper presents a new power conservation scheme for multi-hop ad hoc networks. A virtual backbone consisting of special nodes (coordinators) is used for the power saving algorithm and routing. We present a novel algorithm for constructing a connected dominating set (CDS) that is used to construct and maintain the virtual backbone of the network. Our scheme includes a message history based v...


 Let G be a connected graph. A set S ⊆ V (G) is restrained 2-resolving hop dominating of if and = or ⟨V (G)\S⟩ has no isolated vertex. The domination number G, denoted by γr2Rh(G) the smallest cardinality G. This study aims to combine concept with sets graphs. main results generated in this include characterization join, corona, edge corona lexicographic product graphs, as well their corr...

A critical issue in battery-powered sensor networks is to construct energy efficient virtual backbones for network routing. Recent study in battery technology reveals that batteries tend to discharge more power than needed and reimburse the over-discharged power if they are recovered. In this paper we first provide a mathematical battery model suitable for implementation in sensor networks. We ...

An important question in multi-radio multi-channel and multi-hop networks is how to perform efficient network-wide broadcast. Currently almost all broadcasting protocols assume a single-radio single-channel network model. Simply using them in multi-channel environment without careful enhancement will result in unnecessary redundancy. In this paper, we focus on reducing the amount of redundant t...

Given a simple undirected graph, the minimum connected dominating set problem is to find a minimum cardinality subset of vertices D inducing a connected subgraph such that 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 first proposes a constant-ratio...

Let G = (V,E) be a graph. A subset S ⊆ V is a dominating set of G if every vertex not in S is adjacent to a vertex in S. A set D̃ ⊆ V of a graph G = (V,E) is called an outer-connected dominating set for G if (1) D̃ is a dominating set for G, and (2) G[V \ D̃], the induced subgraph of G by V \ D̃, is connected. The minimum size among all outer-connected dominating sets of G is called the outerconnec...

Weakly connected dominating set (WCDS) has been proposed to cluster mobile ad hoc networks and be used as a virtual backbone. There have been some distributed approximation algorithms proposed in the literature for minimum WCDS. But none of them have constant approximation factors. Thus these algorithms can not guarantee to generate a WCDS of small size. Their message complexities may also be a...

Routing based on a connected dominating set is a promising approach, where the search space for a route is reduced to the hosts in the set. A set is dominating if all the hosts in the system are either in the set or neighbors of hosts in the set. In this paper, we first review a distributed formation of a connected dominating set called marking process and dominating-set-based routing. Then we ...