The <i>k</i>-Metric Dimension of a Unicyclic Graph

Abstract

Given a connected graph G=(V(G),E(G)), a set S⊆V(G) is said to be a k-metric generator for G if any pair of different vertices in V(G) is distinguished by at least k elements of S. A metric generator of minimum cardinality among all k-metric generators is called a k-metric basis and its cardinality is the k-metric dimension of G. We initially present a linear programming problem that describes the problem of finding the k-metric dimension and a k-metric basis of a graph G. Then we conducted a study on the k-metric dimension of a unicyclic graph.

Keywords

• unicyclic graph
• <i>k</i>-metric generator
• <i>k</i>-metric dimension
• <i>k</i>-metric dimensional graph
• linear programming problem