A triangle-free graph is maximal if the addition of any edge produces a triangle. A set S of vertices in a graph G is called an independent dominating set if S is both an independent and a dominating set of G. The independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. In this paper, we show that i(G) ≤ δ(G) ≤ n 2 for maximal triangle-free graph...

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...

I.ABSTRACT WSN is stocked with many small nodes that are highly depends on energy .These nodes offers solutions to many real time problems that are in existence .The capability of these nodes are very limited, mainly for maintaining energy efficiency in WSN .There are various techniques available to effectively maintain the energy in the wireless sensor networks .Among these techniques the most...

Secure clustering problem plays an important role in distributed sensor networks. Weakly Connected Dominating Set (WCDS) is used for solving this problem. Therefore, computing a minimum WCDS becomes an important topic of this research. In this paper, we compare the size of Maximal Independent Set (MIS) and minimum WCDS in unit disk graph. Our analysis shows that five is the least upper bound fo...

In this paper we introduce a general strategy for approximating the solution to minimisation problems in random regular graphs. We describe how the approach can be applied to the minimum vertex cover (MVC), minimum independent dominating set (MIDS) and minimum edge dominating set (MEDS) problems. In almost all cases we are able to improve the best known results for these problems. Results for t...

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...

In ad hoc wireless networks, a connected dominating set can be used as a virtual backbone to improve the performance. Many constructions for approximating the minimum connected dominating set are based on the construction of a maximal independent set. The relation between the sizemis(G) of a maximum independent set and the size cds(G) of a minimum connected dominating set in the same graph G pl...

An independent dominating set D of a graph G = (V,E) is a subset of vertices such that every vertex in V \ D has at least one neighbor in D and D is an independent set, i.e. no two vertices of D are adjacent in G. Finding a minimum independent dominating set in a graph is an NP-hard problem. Whereas it is hard to cope with this problem using parameterized and approximation algorithms, there is ...

In a graph G = (V; E), a set of vertices S is nearly perfect if every vertex in V ? S is adjacent to at most one vertex in S. Nearly perfect sets are closely related to 2-packings of graphs, strongly stable sets, dominating sets and eecient dominating sets. We say a nearly perfect set S is 1-minimal if for every vertex u in S, the set S ? fug is not nearly perfect. Similarly, a nearly perfect s...