Porous Exponential Domination in Harary Graphs

• Published in: Mathematical Notes Vol. 107; no. 1-2; pp. 231 - 237
• Main Authors: Çiftçi, C., Aytaç, A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 2020
• Subjects: Mathematics; Mathematics and Statistics; porous exponential domination; graph theory; Harary graph
• ISSN: 0001-4346; 1573-8876
• DOI: 10.1134/S0001434620010228

A porous exponential dominating set of a graph
G
is a subset
S
such that, for every vertex
v
of
G
, ∑
u
∈
S
(1/2)
d
(
u, v
)−1
≥ l, where
d
(
u, v
) is the distance between vertices
u
and v. The porous exponential domination number, γ
e
*
(G), is the minimum cardinality of a porous exponential dominating set. In this paper, we determine porous exponential domination number of the Harary graph
H
k,n
for all
k
and
n
.