Total domination in maximal outerplanar graphs II

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• 作者：Michael Dorfling^a ; ^{mdorfling@uj.ac.za" class="auth_mail" title="E-mail the corresponding author} ; Johannes H. Hattingh^a ; ^b ; ^{hattinghj@ecu.edu" class="auth_mail" title="E-mail the corresponding author} ; Elizabeth Jonck^a ; ^{ejonck@uj.ac.za" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Outerplanar graph ; Domination ; Total domination
• 刊名：Discrete Mathematics
• 出版年：2016
• 出版时间：6 March 2016
• 年：2016
• 卷：339
• 期：3
• 页码：1180-1188
• 全文大小：447 K

文摘

The total domination number of a graph is the minimum size of a set S$S$ such that every vertex has a neighbor in S$S$. We show that a maximal outerplanar graph of order n≥5$n\ge 5$ has total domination number at most 2n/5$2n/5$, apart from two exceptions, and this bound is best possible.