University of IsfahanTransactions on Combinatorics2251-86573220140601Kernels in circulant digraphs4549477710.22108/toc.2014.4777ENR. LakshmiDepartment of Mathematics,
Annamalai University,
Annamalainagar 608 002
Tamilnadu.S. VidhyapriyaDepartment of Mathematics,
Annamalai University,
Annamalainagar 608 002,
TamilnaduJournal Article20130902A 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.http://toc.ui.ac.ir/article_4777_9925aa9b3c368bb5a7b3527a835e19f9.pdf