| Summary: | 碩士 === 國立中央大學 === 數學研究所 === 86 === The question of partitioning the edges of a simple graph into isomorphic stars has been considered by Yamamoto [3], who obtained a necessary and sufficient condition for an isomorphic star decomposition of complete graphs, and also that of complete bipartite graphs. The isomorphic star decomposition of complete m-partite graph was considered by Ushio [4]. Furthermore, the question of partitioning the edges of multicrowns into isomorphic stars has been solved in [2]. In this paper, we consider the decompositions of the power of a cycle into isomorphic stars.
For a graph G and a positive integer k, let Gk denote the graph with V{Gk) = V{G) and E{Gk) = {uv:u,v εV(G),dG(u,v)≦ k} where dG(u,v) denotes the distance between u and v in G, and Gk is called the k-th power of G. Let Cn denote the cycle on n vertices. In next section, we will obtain the necessary and sufficient condition for Ckn to have an S-decomposition where k < n/2.
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