Porous Exponential Domination in Harary Graphs

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 domin...

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Bibliographic Details
Published inMathematical Notes Vol. 107; no. 1-2; pp. 231 - 237
Main Authors Çiftçi, C., Aytaç, A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 2020
Springer Nature B.V
Subjects
Apexes
Mathematics
Mathematics and Statistics
porous exponential domination
graph theory
Harary graph
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Summary: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 .
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434620010228