The Cayley Sum Graph of Ideals of a Lattice
Let L be a lattice, 𝒥(L) be the set of ideals of L and S be a subset of 𝒥 (L). In this paper, we introduce an undirected Cayley graph of L, denoted by ΓL,S with elements of 𝒥 (L) as the vertex set and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of S su...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2020-12-01
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| Series: | Discussiones Mathematicae - General Algebra and Applications |
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| Online Access: | https://doi.org/10.7151/dmgaa.1332 |
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| author | Afkhami Mojgan Hassankhani Mehdi Khashyarmanesh Kazem |
| author_facet | Afkhami Mojgan Hassankhani Mehdi Khashyarmanesh Kazem |
| author_sort | Afkhami Mojgan |
| collection | DOAJ |
| description | Let L be a lattice, 𝒥(L) be the set of ideals of L and S be a subset of 𝒥 (L). In this paper, we introduce an undirected Cayley graph of L, denoted by ΓL,S with elements of 𝒥 (L) as the vertex set and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of S such that I ∨ K = J or J ∨ K = I. We study some basic properties of the graph ΓL,S such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of ΓL,S. |
| first_indexed | 2024-03-12T05:27:17Z |
| format | Article |
| id | doaj.art-01b0973d9dd64f2192e38f2fb9733f95 |
| institution | Directory Open Access Journal |
| issn | 2084-0373 |
| language | English |
| last_indexed | 2024-03-12T05:27:17Z |
| publishDate | 2020-12-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae - General Algebra and Applications |
| spelling | doaj.art-01b0973d9dd64f2192e38f2fb9733f952023-09-03T07:11:13ZengUniversity of Zielona GóraDiscussiones Mathematicae - General Algebra and Applications2084-03732020-12-0140221723010.7151/dmgaa.1332dmgaa.1332The Cayley Sum Graph of Ideals of a LatticeAfkhami Mojgan0Hassankhani Mehdi1Khashyarmanesh Kazem2Department of Mathematics, University of Neyshabur, P.O. Box 91136-899, Neyshabur, IranDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, IranDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, IranLet L be a lattice, 𝒥(L) be the set of ideals of L and S be a subset of 𝒥 (L). In this paper, we introduce an undirected Cayley graph of L, denoted by ΓL,S with elements of 𝒥 (L) as the vertex set and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of S such that I ∨ K = J or J ∨ K = I. We study some basic properties of the graph ΓL,S such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of ΓL,S.https://doi.org/10.7151/dmgaa.1332latticecayley graphring graphouterplanar graph05c6905c7506b10 |
| spellingShingle | Afkhami Mojgan Hassankhani Mehdi Khashyarmanesh Kazem The Cayley Sum Graph of Ideals of a Lattice Discussiones Mathematicae - General Algebra and Applications lattice cayley graph ring graph outerplanar graph 05c69 05c75 06b10 |
| title | The Cayley Sum Graph of Ideals of a Lattice |
| title_full | The Cayley Sum Graph of Ideals of a Lattice |
| title_fullStr | The Cayley Sum Graph of Ideals of a Lattice |
| title_full_unstemmed | The Cayley Sum Graph of Ideals of a Lattice |
| title_short | The Cayley Sum Graph of Ideals of a Lattice |
| title_sort | cayley sum graph of ideals of a lattice |
| topic | lattice cayley graph ring graph outerplanar graph 05c69 05c75 06b10 |
| url | https://doi.org/10.7151/dmgaa.1332 |
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