Rainbow domination and related problems on strongly chordal graphs.

Abstract: This paper studies a variation of domination in graphs called rainbow domination. For a positive integer , a -rainbow dominating function of a graph is a function such that for any vertex with . The -rainbow domination number of is the minimum value of , where runs over all -rainbow dominating functions of . A related concept is as follows. A weak -dominating function of is a function such that for any vertex with . The weak -domination number of is the minimum value of , where runs over all weak -dominating functions of . In this paper, we prove that for any strongly chordal graph . Our approach is a more general setting called the -function, which leads to interesting results on other variations of domination. We also give a linear-time algorithm for finding the weak -domination numbers of block graphs. [Copyright &y& Elsevier]