Article ID Journal Published Year Pages File Type
6423729 Electronic Notes in Discrete Mathematics 2016 5 Pages PDF
Abstract

Let D=(V,A) be a digraph, an arc subset A′⊆A and a surjective mapping ϕ:A→A′ such that the set of heads of A′ is V and ϕ|A′=Id and for every vertex j∈V, ϕ(ω−(j))⊂ω−(j)∩A′. The partial line digraph of D, LD, is the digraph with vertex set V(LD)=A′ and set of arcs A(LD)={(ij,ϕ(j,k)):(j,k)∈A}. In this paper we prove the following results: Let k,l be two natural numbers such that 1≤l≤k, and D a digraph with δ−(D)≥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

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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