Classification of Efficient Dominating Sets of Circulant Graphs of Degree 5

Classification of Efficient Dominating Sets of Circulant Graphs of Degree 5

For a graph G , a subset D of V ( G ) is called an efficient dominating set of G if D is an independent set and every vertex in V ( G ) \ D is adjacent to exactly one vertex in the set D . In this paper, we give necessary and sufficient conditions for the existence of efficient dominating sets of ci...

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Veröffentlicht in:Graphs and combinatorics 2022-08, Vol.38 (4), Article 120
Hauptverfasser: Kwon, Young Soo, Lee, Jaeun, Sohn, Moo Young
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Engineering Design
Graphs
Mathematics
Mathematics and Statistics
Original Paper
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Zusammenfassung:For a graph G , a subset D of V ( G ) is called an efficient dominating set of G if D is an independent set and every vertex in V ( G ) \ D is adjacent to exactly one vertex in the set D . In this paper, we give necessary and sufficient conditions for the existence of efficient dominating sets of circulant graphs of degree 5 and classify these sets.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-022-02527-6