关于函子图的罗马控制数及其补码

IF 0.1 Q4 MATHEMATICS
E. Vatandoost, Athena Shaminezhad
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引用次数: 0

摘要

摘要设为图和函数,其中每个顶点都有一个顶点,其中Then是罗马控制函数或的a。的权重为。所有函数的最小权重称为的罗马控制数。设为图,G'是的副本。则函数的函数图由其顶点和边分别表示。本文讨论了函子图及其补码的罗马支配数。我们给出了一个通界,其中是一个置换。此外,还考虑了一些特殊图的罗马支配数。我们得到了的一般界,并证明了这个界是尖锐的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On roman domination number of functigraph and its complement
Abstract Let be a graph and be a function where for every vertex with there is a vertex where Then is a Roman dominating function or a of The weight of is The minimum weight of all is called the Roman domination number of denoted by Let be a graph with and G' be a copy of with Then a functigraph with function is denoted by its vertices and edges are and respectively. This paper deals with the Roman domination number of the functigraph and its complement. We present a general bound where is a permutation. Also, the Roman domination number of some special graphs are considered. We obtain a general bound of and we show that this bound is sharp.
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