The k-Metric Dimension of a Unicyclic Graph

Identifier:  imarina:9232638

Handle: https://hdl.handle.net/20.500.11797/imarina9232638

Authors:  Alberto Rodriguez-Velazquez, Juan

Abstract:
Given a connected graph G=(V(G),E(G)), a set S & SUBE;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.