The Bounds on the Locating-Chromatic Number for a Subdivision of a Graph on One Edge

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• 作者：Ira Apni Purwasih ; ^{ira_apni_p@students.itb.ac.id" class="auth_mail" title="E-mail the corresponding author} ; Edy Tri Baskoro ^{ebaskoro@math.itb.ac.id" class="auth_mail" title="E-mail the corresponding author} ; Hilda Assiyatun ^{hilda@math.itb.ac.id" class="auth_mail" title="E-mail the corresponding author} ; Djoko Suprijanto ^{djoko@math.itb.ac.id" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Locating-chromatic number ; subdivision ; pendant
• 刊名：Procedia Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：74
• 期：Complete
• 页码：84-88
• 全文大小：209 K

文摘

The study of locating-chromatic numbers has been done for many classes of graphs. Recently, Behtoei and Anbarloei (2014) presented the locating-chromatic number of wheels. Inspired by the result of Behtoei and Anbarloei, the authors (2012,2013) gave the locating-chromatic number of the subdivision of a wheel on one of its spoke or cycle edges. In this paper, we determine an upper bound on the locating-chromatic number of a subdivision of any connected graph on any one edge and show that the bound is tight. In particular, we give the lower bound for the locating-chromatic number of a subdivision of any graph on a pendant edge. Furthermore, we give the exact values of the locating-chromatic number of a subdivision of a complete and a star graph on any one edge.