Kernel in Oriented Circulant Graphs

A kernel in a directed graph D(V,E) is a set S of vertices of D such that no two vertices in S are adjacent and for every vertex u in $V\smallsetminus S$ there is a vertex v in S , such that (u,v) is an arc of D. The problem of existence of a kernel is NP-complete for a general digraph. In this paper we introduce the strong kernel problem of an undirected graph G and solve it in polynomial time for circulant graphs.

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