Further results on complementary perfect domination number of a graph

G. Mahadevan, B. Ayisha
2013 International Mathematical Forum  
A subset S of V is called a dominating set in G if every vertex in v -S is adjacent to at least one vertex in S. The minimum cardinality taken over all dominating sets in G is called the dominating number of G is denoted by .The conce[pt of complementary perfect domination number of a graph was introduced by Paulraj Joseph. J, Mahadeven. G, Selvam. A in [9] . A subset S of V of a non trivial graph G is said to be complementary perfect dominating set, if S is a dominating set and has a perfect
more » ... and has a perfect matching. The minimum cardinality taken over all complementary perfect dominating sets is called complementary perfect domination number and is denoted by cp. The minimum number of colours required to colour all the vertices of G in such a way that adjacent vertices do not receive the same colour is called the chromatic number and is denoted by χ of G. In [6],the authors characterized the classes of graphs for which the sum of complementary perfect domination number and chromatic number of order upto 2n-5.In this paper we characterize the classes of graphs for which the sum of complementary perfect domination number and chromatic number = 2n-6, for any n>3. Mathematics Subject Classification: 05C
doi:10.12988/imf.2013.13010 fatcat:dm4k6ccz4nambavyxdhwk7vb7e