University of Isfahan Transactions on Combinatorics 2251-8657 3 2 2014 06 01 Kernels in circulant digraphs 45 49 4777 10.22108/toc.2014.4777 EN R. Lakshmi Department of Mathematics, Annamalai University, Annamalainagar 608 002 Tamilnadu. S. Vidhyapriya Department of Mathematics, Annamalai University, Annamalainagar 608 002, Tamilnadu Journal Article 2013 09 02 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  <em>Digraphs‎ - ‎theory‎, ‎algorithms and applications</em>‎, ‎Second Edition‎, ‎Springer-Verlag‎, ‎2009‎, ‎by J‎. ‎Bang-Jensen and G‎. ‎Gutin‎. https://toc.ui.ac.ir/article_4777_9925aa9b3c368bb5a7b3527a835e19f9.pdf