On the Roman domination in the lexicographic product of graphs

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• 作者：Tadeja Kraner &Scaron ; umenjak^a ; ^b ; ¹ ; ^{tadeja.kraner@uni-mb.si} ; Polona Pavli膷^b ; ^{polona.pavlic@imfm.si} ; Aleksandra Tepeh^c ; ¹ ; ^{aleksandra.tepeh@uni-mb.si}
• 关键词：Roman domination ; Total domination ; Lexicographic product
• 刊名：Discrete Applied Mathematics
• 出版年：2012
• 期刊代码：46_0166218x
• 类别：cp
• 出版时间：September, 2012
• 卷：160
• 期：13-14
• 页码：2030-2036
• 文件大小：218 K

摘要

A Roman dominating function of a graph is a function such that every vertex with is adjacent to some vertex with . The Roman domination number of is the minimum of over all such functions. Using a new concept of the so-called dominating couple we establish the Roman domination number of the lexicographic product of graphs. We also characterize Roman graphs among the lexicographic product of graphs.