Garijo, Delia and González, Antonio and Márquez, Alberto - 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 Delia

Authors: Garijo, Delia and González, Antonio and Márquez, Alberto

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.


Source : oai:HAL:hal-00966384v1
Volume: Vol. 15 no. 3
Section: Graph Theory
Published on: December 10, 2013
Submitted on: September 2, 2013
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


Share

Browsing statistics

This page has been seen 43 times.
This article's PDF has been downloaded 55 times.