A subset of vertices D of a graph G is a dominating set for G if every vertex of G not in D is adjacent to one in D. A dominating set for G is a connected dominating set if it induces a connected subgraph of G. The connected domination number of G, denoted by γc(G), is the minimum cardinality of a connected dominating set. Graph G is said to be k−γc−critical if γc(G) = k but γc(G+e) < k for eac...

Wedesign fast exponential time algorithms for some intractable graph-theoretic problems. Ourmain result states that aminimum optional dominating set in a graph of order n can be found in time O∗(1.8899n). Ourmethods to obtain this result involvematching techniques. The list of the considered problems includes Minimum Maximal Matching, 3Colourability, Minimum Dominating Edge Set, Minimum Connect...

We describe some new, simple and apparently general methods for designing FPT algorithms, and illustrate how these can be used to obtain a significantly improved FPT algorithm for the Maximum Leaf Spanning Tree problem. Furthermore, we sketch how the methods can be applied to a number of other well-known problems, including the parametric dual of Dominating Set (also known as Nonblocker), Matri...

Connected Dominating Set (CDS) problem in unit disk graph has a significant impact on an efficient design of routing protocols in wireless sensor networks. In this paper, an algorithm is proposed for finding Minimum Connected Dominating Set (MCDS) using Dominating Set. Dominating Sets are connected by using Steiner tree. The algorithm goes through three phases. In first phase Dominating Sets ar...

An odd dominating set of a simple, undirected graph G = (V,E) is a set of vertices D ⊆ V such that |N [v]∩D| ≡ 1 mod 2 for all vertices v ∈ V . It is known that every graph has an odd dominating set. In this paper we consider the concept of connected odd dominating sets. We prove that the problem of deciding if a graph has a connected odd dominating set is NP-complete. We also determine the exi...

In ad hoc mobile wireless networks due to host mobility broadcasting is expected to be more frequently used to nd a route to a particular host to page a host and alarm all hosts A straight forward broadcasting by ooding is usually very costly and will result in substantial redundancy and more energy consumption Power consumption is an important issue since most mobile hosts operate on battery B...

Let $G$ be a connected graph. A set $S$ of vertices in is 1-movable 2-resolving hop dominating if and for every $v \in S$, either $S\backslash \{v\}$ or there exists vertex $u \big((V (G) \backslash S) \cap N_G(v)\big)$ such that $\big(S \{v\}\big) \cup \{u\}$ $G$. The domination number $G$, denoted by $\gamma^{1}_{m2Rh}(G)$ the smallest cardinality In this paper, we investigate concept study i...