Author:
Joeshi Annie Vetha V.,A. Anto Kinsley
Abstract
Abstract
Let D = (V, A) be a finite and simple directed graph (digraph) with vertex set V and arc set A. For an integer k ≥ 1, the out k-neighborhood of a vertex ν is defined as
N
k
+
(
ν
)
=
{
u
∈
V
(
D
)
/
d
→
(
ν
,
u
)
≤
k
}
. A set S ⊆ V is said to be a distance k-dominating set in D if N+
k
(S) ∪ S = V. The minimum distance k-dominating set in D is the distance k-domination number,
γ
k
→
(
D
)
. For two integers s ≥ 2 and k, the (s, k) - kernal set and the (s, k) - kernal number,
ξ
k
→
(
D
)
are studied. This parameter
ξ
k
→
(
D
)
is also computed for different types of digraphs. Strong digraphs (SDs) are studied and
γ
k
→
(
D
)
of SDs are determined in terms of the radius and diameter of SDs. Also (2, k) - kernals of directed wounded spider are classified with
ξ
k
→
(
D
)
. Some upper and lower bounds on
γ
k
→
(
D
)
are determined and characterized some digraphs achieving these bounds.
Subject
General Physics and Astronomy
Reference8 articles.
1. Semikernals and (k, l) - kernals in digraphs;Galeana-Snchez;SIAM J. Discrete Math,1998