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- Title
The Regular Digraph Associated to a Poset.
- Authors
Afkhami, M.; Bahrami, S.; Khashyarmanesh, K.
- Abstract
Let (P , ≤) be a partially ordered set with a least element 0. The regular digraph of ideals of P, denoted by Γ → (P) , is a digraph whose vertex-set is the set of all nontrivial ideals of P and, for every two distinct vertices I and J, there is an arc from I to J whenever I contains a nonzero zero-divisor on J. Also, the undirected regular graph of ideals of P, denoted by Γ (P) , is a graph with all nontrivial ideals of P being the vertex-set, and for two distinct vertices I and J, I is adjacent to J if and only if I contains a nonzero zero-divisor on J or J contains a nonzero zero-divisor on I. In this paper, we study some basic properties of Γ → (P) . Also we completely characterize all posets P with planar regular graph.
- Subjects
PLANAR graphs; DIVISOR theory; PARTIALLY ordered sets; REGULAR graphs; UNDIRECTED graphs
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2019, Vol 42, Issue 3, p995
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-017-0530-8