@Article{Mojdeh2009,
author = "Mojdeh, Doost Ali and Mirzamani, Somayeh",
title = "On the diameter of dot-critical graphs",
journal = "Opuscula Math.",
year = "2009",
volume = "29",
number = "2",
pages = "165--175",
doi = "http://dx.doi.org/10.7494/OpMath.2009.29.2.165",
url = "http://dx.doi.org/10.7494/OpMath.2009.29.2.165",
abstract = "A graph G is \(k\)-dot-critical (totaly \(k\)-dot-critical) if \(G\) is dot-critical (totaly dot-critical) and the domination number is \(k\). In the paper [T. Burtona, D. P. Sumner, Domination dot-critical graphs, Discrete Math, 306 (2006), 11-18] the following question is posed: What are the best bounds for the diameter of a \(k\)-dot-critical graph and a totally \(k\)-dot-critical graph \(G\) with no critical vertices for \(k \geq 4\)? We find the best bound for the diameter of a \(k\)-dot-critical graph, where \(k \in\{4,5,6\}\) and we give a family of \(k\)-dot-critical graphs (with no critical vertices) with sharp diameter \(2k-3\) for even \(k \geq 4\).",
keywords = "dot-critical graph, diameter",
issn = "1232-9274"
}