Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423729 | Electronic Notes in Discrete Mathematics | 2016 | 5 Pages |
Abstract
Let D=(V,A) be a digraph, an arc subset Aâ²âA and a surjective mapping Ï:AâAâ² such that the set of heads of Aâ² is V and Ï|Aâ²=Id and for every vertex jâV, Ï(Ïâ(j))âÏâ(j)â©Aâ². The partial line digraph of D, LD, is the digraph with vertex set V(LD)=Aâ² and set of arcs A(LD)={(ij,Ï(j,k)):(j,k)âA}. In this paper we prove the following results: Let k,l be two natural numbers such that 1â¤lâ¤k, and D a digraph with δâ(D)â¥1. Then the number of (k,l)-kernels of D is less than or equal to the number of (k,l)-kernels of LD. Moreover, if l
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Mucuy-kak Guevara, Camino Balbuena, Hortensia Galeana-Sánchez,