GEO CHROMATIC NUMBER FOR CERTAIN PRODUCT GRAPHS
Joseph Paul.R1, Chitra Ramaprakash2
1Assistant Professor, SNS College of Engineering (Autonomous), Coimbatore – 641 101, India.
2Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore, India.
Abstract: The distance between two nodes x1, x2 contained in V(G) is the minimum size of x1 – x2 paths in G. An x1 – x2 path of the size dG(x1, x2) is known as geodesic. We indicate IG(x1, x2) as the set of nodes which are lies inside some x1 – x2 geodesics of G. A node is said to lie on x1 – x2 geodetic if c is an inner node of P. The bounded interval I(x1, x2) includes x1, x2 and all nodes lying on some x1 – x2 geodesic of G. Consider a non- empty set S V(G). For a set I(S) = . If G is connected graph, thus S is a geodetic set with the condition that I(S) = V (G) [2]. The minimum cardinality S of G is called geodetic number defined by g(G). A j – node coloring of G is an allotment of j colors to the nodes of G. The coloring is proper if no two joining nodes accept same color such that = j is said to be j – chromatic, where j k. a minimum cardinality of a chromatic number of G is called chromatic set [1, 3, 4]. Beulah Samli and Robinson Chellathurai [9] introduced the concepts of the Geo Chromatic number of graph. In this paper, we consider a graph to be connected, finite, simple where V(G) is node set and E(G) is link set [5,6]. In this paper, we have defined geo chromatic number for certain graph and have discussed few results.
Keywords: Geodetic Number,Geo chromatic number, Lexicographic product, Tensor Product, Co-Normal Product