[A.Sasireka, 4(4): April, 2015] ISSN: 2277-9655 Scientific Journal Impact Factor: 3.449 (ISRA), Impact Factor: 2.114 http: // www.ijesrt.com© International Journal of Engineering Sciences & Research Technology [24] IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY OPTIMIZATION OF NODE FIXING IN WIRELESS SENSOR NETWORK USING CONNECTED DOMATIC NUMBER OF A GRAPH A. Sasireka * , P. Vijayalakshmi, A. H. Nandhu Kishore *, ** Department of Mathematics, P.S.N.A.College of Engineering and Technology, Dindigul, TamilNadu, India – 624 622. ***Department of Computer Science and Engineering, P.S.N.A.College of Engineering and Technology, Dindigul, TamilNadu, India – 624 622. Abstract Wireless Sensor Network (WSN) is composed of miniature sensor devices which include tiny sensor and small batteries with energy, computation and communication constraints. Care must be taken in placing the nodes for effective optimization of accessing the resources in the network. In this paper, merging of two arbitrary wireless sensor network is considered and aims at optimizing the placement of nodes by utilizing the concept of connected domatic number of a graph. Keywords: Wireless Sensor Network, Dominating Set, Domatic Number, Connected Domatic set, Domatic Partition. Introduction Graph theory is one of the hottest research areas of modern mathematics which has seen a magnificent growth due to the number of applications in computer and communication, molecular physics and chemistry, social networks, biological sciences, computational linguistics, and in other numerous fields. In graph theory, one of the extensively researched branches is domination in graph. In graph theory, a set S  V is said to be a dominating set, if every vertex in V-S is adjacent to at least one vertex in S. The minimum cardinality taken over all minimal dominating set is called the domination number of G and is denoted by (G) [1]. A dominating set is called a connected dominating set if the subgraph <S> induced by S is connected. The connected domination number  c (G) is the minimum number of vertices in a connected dominating set in graph G [2]. A domatic partition of a graph G=(V,E) is a partition of V into disjoint sets V 1 ,V 2 ,V 3 ,…V k such that each V j is a dominating set for G. The maximum number of dominating sets in which the vertex set of a graph G can be partitioned is called the domatic number of graph G, and it is denoted by dom(G) or d(G) [3]. The concept of domatic partitioning plays an important role in locating the resources in a network. Let us assume that a node in the network can access only the resources present in the neighboring nodes or itself. A network may contain several essential types of resources to be used. If a particular resource is needed to be accessed from every node, then, the dominating set of the network must possess the copy of that resource. This particular resource which is to be accessed must occupy the dominating set of the network. If each node has bounded capacity, the amount of resource to be occupied in a node is limited. If each node can hold only a single resource then the dominating set will support the maximum number of resources which is equal to the domatic number of the graph [4]. Characterization of Connected Domatic Number We review some elementary facts about dominating sets and domatic partitions, in light of the novelty of the problem for many readers.