RESTRAINED GEO CHROMATIC NUMBER OF A SOME GRAPHS

Abstract

A set S of vertices is a geodetic set if  The minimum cardinality of a geodetic set is the geodetic number of G and is denoted by A set S of vertices in G is a restrained geodetic set if S is a geodetic set and the subgraph  induced be  has no isolated vertex. A subset  is said to be a geo chromatic set if S is both a geodetic and a chromatic set of G. A subset  is a restrained geo chromatic set of G if S is a geo chromatic set and the subgraph  induced by  has no isolated vertex. The minimum cardinality of a restrained geo chromatic number of G and is denoted by  In this paper, we determine bounds for it and characterize graphs which realize these bounds for some known graphs.