Alejandro Estrada-Moreno

The k -metric dimension of the lexicographic product of graphs

Given a simple and connected graph G = ( V , E ) , and a positive integer k , a set S ? V is said to be a k -metric generator for G , if for any pair of different vertices u , v ? V , there exist at least k vertices w 1 , w 2 , ? , w k ? S such that d G ( u , w i ) ? d G ( v , w i ) , for every i ? { 1 , ? , k } , where d G ( x , y ) denotes the distance between x and y . The minimum cardinality of a k -metric generator is the k -metric dimension of G . A set S ? V is a k -adjacency generator for G if any two different vertices x , y ? V ( G ) satisfy | ( ( N G ( x ) ? N G ( y ) ) ? { x , y } ) ? S | ? k , where N G ( x ) ? N G ( y ) is the symmetric difference of the neighborhoods of x and y . The minimum cardinality of any k -adjacency generator is the k -adjacency dimension of G . In this article we obtain tight bounds and closed formulae for the k -metric dimension of the lexicographic product of graphs in terms of the k -adjacency dimension of the factor graphs.

On Generalized Sierpi\'{n}ski Graphs

Abstract In this paper we obtain closed formulae for several parameters of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. In particular, we focus on the chromatic, vertex cover, clique and domination numbers.

The Simultaneous Strong Metric Dimension of Graph Families

Let

The Simultaneous Metric Dimension of Families Composed by Lexicographic Product Graphs

\mathcal{G}

k-metric resolvability in graphs

G be a family of graphs defined on a common (labelled) vertex set V. A set

Weak Total Resolvability In Graphs

S\subset V