Kernels in circulant digraphs

Document Type: Research Paper

Authors

1 Department of Mathematics, Annamalai University, Annamalainagar 608 002 Tamilnadu.

2 Department of Mathematics, Annamalai University, Annamalainagar 608 002, Tamilnadu

Abstract

A kernel $J$ of a digraph $D$ is an independent set of vertices of $D$ such that for every vertex $w\,\in\,V(D)\,\setminus\,J$ there exists an arc from $w$ to a vertex in $J.$‎ ‎In this paper‎, ‎among other results‎, ‎a characterization of $2$-regular circulant digraph having a kernel is obtained‎. ‎This characterization is a partial solution to the following problem‎: ‎Characterize circulant digraphs which have kernels; it appeared in the book  Digraphs‎ - ‎theory‎, ‎algorithms and applications‎, ‎Second Edition‎, ‎Springer-Verlag‎, ‎2009‎, ‎by J‎. ‎Bang-Jensen and G‎. ‎Gutin‎.

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