期刊名称：International Journal of Innovative Research in Science, Engineering and Technology
印刷版ISSN：2347-6710
电子版ISSN：2319-8753
出版年度：2017
卷号：6
期号：10
页码：19374
DOI：10.15680/IJIRSET.2017.0610009
出版社：S&S Publications
摘要：Let f :V 0,1,2 be a function having the property that for every vertex v V with f v 0 ,there exists a neighbourhood uN v with f u 2 . Such a function is called a Roman dominating function orjust an RDF. The weight of an RDF is the value u V f V f u . The minimum weight of an RDF on G iscalled the Roman domination number of G and is denoted by G R . The function f :V 0 , 1 , 2 , 3 isnamed a Strong Roman dominating function on a graph G whenever for each vertex u with f u 0 there existsan adjacent vertex v to u such that f v 3 . Also for each vertex u with f u 1 there should be at least anadjacent vertex v to u weighted 2. The weight of an SRDF is the value u Vf V f u . Strong Romandomination number of graph G which we denoted by G SR is minimum weight of an SRDF on G . In this paper,we show that .3221 G G G SR R SR And we study the Roman and Strong Roman domination of the trees and we show that T T R SR 3 2 .
关键词：Roman domination; Strong Roman domination; Tree.
