Resumen de Some characterization theorems on dominating chromatic partition-covering number of graphs

L. Benedict Michael Raj, S. K. Ayyaswamy

• Let G = (V, E) be a graph of order n = |V| and chromatic number (G) A dominating set D of G is called a dominating chromatic partition-cover or dcc-set, if it intersects every color class of every X-coloring of G. The minimum cardinality of a dcc-set is called the dominating chromatic partition-covering number, denoted dcc(G). The dcc-saturation number equals the minimum integer i such that every vertex ν ∈ V is contained in a dcc-set of cardinality k.This number is denoted by dccs(G) In this paper we study a few properties ofthese two invariants dcc(G) and dccs(G)