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- Title
An algebraic approach to sets defining minimal dominating sets of regular graphs.
- Authors
Nasernejad, Mehrdad
- Abstract
The article explores the algebraic approach to defining minimal dominating sets of regular graphs. It introduces the concepts of closed neighborhood ideals and dominating ideals of graphs and discusses their properties. The main result of the article states that there exists a regular graph with a given set of minimal dominating sets if certain conditions are satisfied by the associated incidence matrix. The article provides a proof of this result and discusses its implications. It also presents a theorem and an example to illustrate the concept of minimal dominating sets in regular graphs.
- Subjects
REGULAR graphs; DOMINATING set; GRAPH theory; MODULES (Algebra); COMMUTATIVE algebra; NOETHERIAN rings
- Publication
Electronic Journal of Graph Theory & Applications, 2023, Vol 11, Issue 2, p401
- ISSN
2338-2287
- Publication type
Article
- DOI
10.5614/ejgta.2023.11.2.5