Delia Garijo ; Antonio González ; Alberto Márquez - The resolving number of a graph Delia

dmtcs:615 - Discrete Mathematics & Theoretical Computer Science, December 10, 2013, Vol. 15 no. 3 -
The resolving number of a graph DeliaArticle

Authors: Delia Garijo 1; Antonio González ORCID1; Alberto Márquez 1

  • 1 Department of Applied Mathematics I [Sevilla]

We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by Chartrand, Poisson and Zhang. First, we establish an important difference between the two parameters: while computing the metric dimension of an arbitrary graph is known to be NP-hard, we show that the resolving number can be computed in polynomial time. We then relate the resolving number to classical graph parameters: diameter, girth, clique number, order and maximum degree. With these relations in hand, we characterize the graphs with resolving number 3 extending other studies that provide characterizations for smaller resolving number.

Volume: Vol. 15 no. 3
Section: Graph Theory
Published on: December 10, 2013
Accepted on: June 9, 2015
Submitted on: September 2, 2013
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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