Bounds for metric dimensions of generalized neighborhood corona graphs

Abstract

In this paper, the authors analysed metric dimensions of arbitrary graphs G★˜∧i=1|V(G)|Hi in which graphs G,H1,H2,…,H|V(G)| are non-trivial, G is connected, and ★˜ denotes generalized neighborhood corona operation. We found lower bounds of dim(G★˜∧i=1|V(G)|Hi) as function of dimA(Hi) where dimA(Hi) denotes adjacency metric dimensions of Hi. We also found upper bounds of dim(G★˜∧i=1|V(G)|Hi) when G does not contain pair of false twin vertices. Furthermore, we found a characteristic of dim(G★˜∧i=1|V(G)|Hi) which indicates that our lower bounds are strict.

Keywords

• Neighborhood corona graph
• Metric dimension
• Resolving set