The Roman k-domatic Number of a Graph

作     者：Seyed Mahmoud SHEIKHOLESLAMI Lutz VOLKMANN 

作者机构：Department of Mathematics Azarbaijan University of Tarbiat MoaUem Tabriz 53714-161 L R. Iran and School of Mathematics Institute for Research in Fundamental Sciences ( IPM) Lehrstuhl H fiir Mathematik RWTH Aachen University 52056 Aachen Germany 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2011年第27卷第10期

页      面：1899-1906页

核心收录：

学科分类：07[理学] 08[工学] 080203[工学-机械设计及理论] 0802[工学-机械工程] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：IPM 

主　　题：Roman domination number Roman domatic number Roman k-domination number Ro- man k-domatic number 

摘      要：Let k be a positive integer. A Roman k-dominating function on a graph G is a labeling f ： V（G） → {0, 1, 2} such that every vertex with label 0 has at least k neighbors with label 2. A set {f1, f2,..., fd} of distinct Roman k-dominating functions on G with the property that ∑di=1 fi（v） ≤ 2 for each v C V（G）, is called a Roman k-dominating family （of functions） on G. The maximum number of functions in a Roman k-dominating family on G is the Roman k-domatic number of G, denoted by dkR（G）. Note that the Roman 1-domatic number dlR（G） is the usual Roman domatic number dR（G）. In this paper we initiate the study of the Roman k-domatic number in graphs and we present sharp bounds for dkR（G）. In addition, we determine the Roman k-domatic number of some graphs. Some of our results extend those given by Sheikholeslami and Volkmann in 2010 for the Roman domatic number.