R. Lakshmi - Department of Mathematics, Annamalai University, Annamalainagar ۶۰۸ ۰۰۲ Tamilnadu.
S. Vidhyapriya - Department of Mathematics, Annamalai University, Annamalainagar ۶۰۸ ۰۰۲, Tamilnadu

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 ۲-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, ‎۲۰۰۹‎, ‎by J‎. ‎Bang-Jensen and G‎. ‎Gutin‎.

Kernel, Symmetric Digraphs, Circulant Digraph