In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous
KEYWORDS
Homogeneous, Mobile Ad hoc networks, Double star, Leader node, Relative closeness relationship
AD HOC NETWORKS -A BRIEF REVIEWAn ad hoc wireless network is a collection of two or more devices (also termed as nodes) equipped with wireless communications and networking capability. Such devices/nodes can communicate either directly or through intermediate nodes depending on the availability of the nodes within or outside the radio range. An ad hoc network is self-organizing and adaptive, i.e, the already formed network can be de-formed on-the-fly without the need for any central administration. The nodes in an ad hoc network must be capable of identifying the connectivity with the neighbouring nodes, so as to allow communication and sharing of information and services. The nodes must perform routing and packet-forwarding functions. The topology changes continuously as the devices are not tied down to specific locations over time. Hence, the most important and challenging issues in a mobile ad hoc network are the mobile nature of the devices, scalability and constraints on resources such as limited bandwidth, limited and varying battery power, etc. Depending on the nature of devices, the uniformity in transmission range and network architecture, the network can either be homogeneous or heterogeneous. The network considered in this paper is a homogeneous where each node is assumed to have uniform transmission range.
SIGNIFICANCE OF CLUSTERINGA cluster is a subset of nodes of a network. Clustering is the process of partitioning a network into clusters and it is a way of making ad hoc networks more scalable. Scalability refers to the network's capability to facilitate efficient communication even in the presence of large number of network nodes. Cluster-based structures promote more efficient usage of resources in controlling large dynamic networks. With cluster-based control structures, the physical network
Given a graph G, a subset S of vertices of G is an efficient dominating setIn general, not every graph is efficiently dominatable. Further, the class of efficiently dominatable graphs has not been completely characterized and the problem of determining whether or not a graph is efficiently dominatable is NP-Complete. Hence, interest is shown to study the efficient domination property for graphs under restricted conditions or special classes of graphs. In this paper, we study the notion of efficient domination in some Lattice graphs, namely, rectangular grid graphs (P m 2P n ), triangular grid graphs, and hexagonal grid graphs.
The concept of network is predominantly used in several applications of computer communication networks. It is also a fact that the dominating set acts as a virtual backbone in a communication network. These networks are vulnerable to breakdown due to various causes, including traffic congestion. In such an environment, it is necessary to regulate the traffic so that these vulnerabilities could be reasonably controlled. Motivated by this, [Formula: see text]-part degree restricted domination is defined as follows. For a positive integer [Formula: see text], a dominating set [Formula: see text] of a graph [Formula: see text] is said to be a [Formula: see text]-part degree restricted dominating set ([Formula: see text]-DRD set) if for all [Formula: see text], there exists a set [Formula: see text] such that [Formula: see text] and [Formula: see text]. The minimum cardinality of a [Formula: see text]-DRD set of a graph [Formula: see text] is called the [Formula: see text]-part degree restricted domination number of [Formula: see text] and is denoted by [Formula: see text]. In this paper, we present a polynomial time reduction that proves the NP -completeness of the [Formula: see text]-part degree restricted domination problem for bipartite graphs, chordal graphs, undirected path graphs, chordal bipartite graphs, circle graphs, planar graphs and split graphs. We propose a polynomial time algorithm to compute a minimum [Formula: see text]-DRD set of a tree and minimal [Formula: see text]-DRD set of a graph.
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