The resolving number of a graph Delia
2013 ◽
Vol Vol. 15 no. 3
(Graph Theory)
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Keyword(s):
Np Hard
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Graph Theory International audience 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.
2011 ◽
Vol Vol. 13 no. 1
(Graph and Algorithms)
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2005 ◽
Vol DMTCS Proceedings vol. AE,...
(Proceedings)
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Keyword(s):
2010 ◽
Vol Vol. 12 no. 1
(Graph and Algorithms)
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2008 ◽
Vol Vol. 10 no. 1
(Graph and Algorithms)
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2009 ◽
Vol Vol. 11 no. 2
(Graph and Algorithms)
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Keyword(s):
2014 ◽
Vol Vol. 16 no. 3
(Graph Theory)
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Keyword(s):
2017 ◽
Vol 09
(02)
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pp. 1750024
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