Constructing Many-to-One Vertex-Disjoint Paths in (n, k)-Star Graphs
نویسندگان
چکیده
An Sn,k refers to a generalized version of an n-star graph (Sn), where Sn,n−1 and Sn are isomorphic and Sn,1 is obviously a complete graph of n vertices (Kn). This study constructs a set of many-to-one vertex-disjoint paths in an (n, k)-star graph (Sn,k), and computes the upper bound of Rabin number of an Sn,k, where 2≤k≤n−1. The upper bound of the Rabin number of an Sn,k is calculated by constructing a maximal number of many-to-one vertex-disjoint paths from a set of n−1 distinct destination vertices to a source vertex in it. This work reveals that if k=2, the Rabin number of an Sn,k is bounded above by its diameter plus 2, and if k≥3, bounded by its diameter plus 4 (or 3) for n/2+1≤k≤n−1 and n is even (or otherwise).
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