A Study on Mixed Inverse Center-Smooth Set of Some Graphs and its application

For S is a dominating set of G and V-S V(G) of a center smooth graph Gis called amixed inverse center smooth set if (i) For every vεV-S, |N[v]∩V(G)| 1(mod p) and (ii) Every elementuεS is either adjacent or incident to an element of V-S. The number of vertices in a mixed inversecenter smooth set is called the mixed inverse center smooth number and it is denoted by γmcs(G).Inthis paper, we introduce the new concept of mixed inverse center smooth number and establish someresults on this new parameter. Also, we determine the bounds of γmcs- set of some graph classes.