NON-SPLIT GEODETIC DOMINATION NUMBER OF A SOME GRAPHS

Abstract

A set of vertices S in a graph G is a dominating set of each vertex of G is determined by some vertex in S.The domination number ????(????) of G is the minimum cardinality of a dominating set of G. A set S of vertices isa geodetic set of G if ????[????]=????(????) and the minimum cardinality of such set is geodetic number and is denotedby ????(????). A subset S of ????(????) is a geodetic dominating set of G if S is a geodetic set and a dominating set of G.The minimum cardinality of geodetic dominating set is called the geodetic domination number of G and isdenoted by ????????(????). A set ????⊆????(????) is called a non-split geodetic dominating set if S is a geodetic and adominating set and also <????(????)−????> is connected. The minimum cardinality of non-split geodetic dominatingset of G is called the non-split geodetic domination number of G and is denoted by ????????????????(????). In this paper wedetermined the non-split geodetic domination number of some graphs.