Volume :1 , Issue :1 ,Page :29-42

Abstract :Let G be a simple graph with vertex set V(G) and edge set E(G). A Set S  V is said to be a chromatic preserving set or a cp-set if χ () = χ (G) and the minimum cardinality of a cp-set in G is called the chromatic preserving number or cp-numbe r of G and is denoted by cpn(G). A cp-set of cardinality cpn(G) is called a cpn-set. A partition of V(G) is said to be a cp-partition, if each subset in the partition induces a chromatic preserving set (c p-set). The cp-partition number of a graph G is defined to be the maximum cardinality of a cp-partitio n of V(G) and is denoted by cppn(G). In this paper, cp-number and cp-partition numb er of some standard graphs are found. Some of the graphs for which cpn(G) = χ (G) are identified. Some Nordhaus-Gaddum ty pe of results are obtained for cp- number and cp-partition number.