Metric and edge-metric dimensions of bobble-neighbourhood-corona graphs

Resolving set in a graphG =(V(G), E(G)) is an ordered subset W of V(G) such that every vertex in V(G) has distinct representation with respect to W. Resolving set of G of minimum cardinality is called basis of G.Cardinality of basis of G is called metric dimension of G, dim(G). An ordered set W is called edge resolving set of G if every edge in E(G) has distinct edge-representation with respect to W. Edge-resolving sets in a graph Gof minimum cardinality is called edge-metric basis of G. Cardinality of edge-basis of G is called as edge-metric dimension of G, edim(G). Neighbourhood corona of G and H, G*H, is agraph obtained by taking graph G and |V (G)| graph Hi with Hi i = 1,2,..., |7(G)| is copy of H, then all vertices in H are connected with neighbouring vertex of vertex v in V (G). In this paper, we determine and analyse metric and edge-metric dimension of bobble-neighbourhood-corona, that is metric and edge-metric dimension of neighbourhood-corona of G and H, G*H, with H is trivial graph K1, and G ? {Cn,Kn}.