Bounds for metric dimensions of generalized neighborhood corona graphs

In this paper, the authors analysed metric dimensions of arbitrary graphs G (star) over tilde boolean AND H-vertical bar V(G)vertical bar(i=1)i in which graphs G, H-1, H-2, ..., H-vertical bar V(G)vertical bar are non-trivial, G is connected, and (star) over tilde denotes generalized neighborhood corona operation. We found lower bounds of dim (G (star) over tilde boolean AND H-vertical bar V(G)vertical bar(i=1)i) as function of dim(A)(H-i) where dim(A)(H-i) denotes adjacency metric dimensions of H-i. We also found upper bounds of dim (G (star) over tilde boolean AND H-vertical bar V(G)vertical bar(i=1)i) when G does not contain pair of false twin vertices. Furthermore, we found a characteristic of dim (G (star) over tilde boolean AND H-vertical bar V(G)vertical bar(i=1)i) which indicates that our lower bounds are strict.

Automated summary

This paper analyzes the metric dimensions of arbitrary graphs and the generalized neighborhood corona operation. It provides lower and upper bounds of metric dimensions, as well as a characteristic indicating the strictness of the lower bounds.