Upper Bounds on k-rainbow Domination Number of Sierpiński Graphs

• Main Authors: Ting-Wei Liu, 劉庭崴
• Other Authors: Kung-Jui Pai
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/edz49c

碩士 === 明志科技大學 === 工業工程與管理系碩士班 === 102 === The k-rainbow domination is a variant of the classical domination problem in graphs and is defined as follows. Given an undirected graph G = (V, E), we have a set C with k colors and assign an arbitrary subset of these colors to each vertex of G. If a vertex is assigned an empty set, then the union of color sets of its neighbors must be C. This assignment is called the k-rainbow dominating function of G. The minimum sum of numbers of assigned colors over all vertices of G is called the k-rainbow domination number of G. In this paper, we give some algorithms to determine the k-rainbow dominating sets on Sierpiński graphs with k ∈ {2, 3, 4}, and we have the upper bounds of k-rainbow domination number on Sierpiński graph where k ∈ {2, 3, 4}.