• Geodomination, g-independence and g-irredundance

Abstract

The concept of geodetic set was introduced by F. Buckley and F.Harary in [1] and   G.Chartrand , F.Harary and  P.Zhang  in [2]. In [4], the geodetic number was defined by F.Harary, E.Loukakis and C.Tsouros. In this paper, we introduce the concept of geodetic neighbourhood(g-neighborhood)  and closed geodetic neighbourhood sets of a pair of vertices of a connected graph G with atleast two vertices. And, we define the geodetic number of a graph using         g-neighbourhood sets. Further, we introduce some new concepts such as g-isolated vertices, g-independence,               g-independence number, g-connectedness of a graph, g-independent geodetic set, g-independent geodetic number,       g-irredundance number etc. Results connecting the above defined parameters are developed.