• R. Lakshmi
• S. Vidhyapriya

A kernel J of a digraph D is an independent set of vertices of D such that for every vertex w∈V(D)J there exists an arc from w to a vertex in J. Let D be a digraph with vertex set V={v_1,v_2,…,v_n} and let D_1,D_2,…,D_n be digraphs which are pairwise vertex-disjoint. The composition digraph D_0=D[D_1,D_2,…,D_n ] is the digraph with vertex set V(D_1)∪V(D_2)∪…∪V(D_n) and arc set (⋃_(i=1)^n▒〖A(D_i))〗 ⋃▒‍ {(x,y): x∈V(D_i ),y∈V(D_j ),i≠j,(v_i,v_j )∈A(D)}. In this paper, we have characterized the existence of kernels in D_0. More precisely, D_0 contains a kernel if, and only if, the digraph D contains a kernel {v_(i_1 ),v_(i_2 ),…,v_(i_k )} such that each of the digraphs D_(i_1 ),D_(i_2 ),…,D_(i_k ) contains a kernel.

Kernel, composition of digraphs

"Kernels in composition of digraphs ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 1, page no.317-319, January-2019, Available :http://www.jetir.org/papers/JETIR1901341.pdf

"Kernels in composition of digraphs ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 1, page no. pp317-319, January-2019, Available at : http://www.jetir.org/papers/JETIR1901341.pdf