DC Field | Value | Language |
---|---|---|
dc.contributor.author | Damnjanović, Ivan | en_US |
dc.contributor.author | Stevanović, Dragan | en_US |
dc.date.accessioned | 2021-11-08T15:31:51Z | - |
dc.date.available | 2021-11-08T15:31:51Z | - |
dc.date.issued | 2022-01-15 | - |
dc.identifier.issn | 0024-3795 | - |
dc.identifier.uri | http://researchrepository.mi.sanu.ac.rs/handle/123456789/4678 | - |
dc.description.abstract | A nut graph is a simple graph whose adjacency matrix has the eigenvalue 0 with multiplicity 1 such that its corresponding eigenvector has no zero entries. Motivated by a question of Fowler et al. (2020) [5] to determine the pairs (n,d) for which a vertex-transitive nut graph of order n and degree d exists, Bašić et al. (2021) [1] initiated the study of circulant nut graphs. Here we first show that the generator set of a circulant nut graph necessarily contains equally many even and odd integers. Then we characterize circulant nut graphs with the generator set {x,x+1,x+2,…,x+2t−1} for x,t∈N, which generalizes the result of Bašić et al. for the generator set {1,2,3,…,2t}. We further study circulant nut graphs with the generator set {1,2,3,…,2t+1}∖{t}, which yields nut graphs of every even order n≥4t+4 whenever t is odd such that t≢101 and t≢1815. This fully resolves Conjecture 9 from Bašić et al. (2021) [1]. We also study the existence of 4t-regular circulant nut graphs for small values of t, which partially resolves Conjecture 10 of Bašić et al. (2021) [1]. | en_US |
dc.publisher | Elsevier | en_US |
dc.relation.ispartof | Linear Algebra and Its Applications | en_US |
dc.subject | Circulant graphs | Cyclotomic polynomials | Graph eigenvalues | en_US |
dc.title | On circulant nut graphs | en_US |
dc.type | Article | en_US |
dc.identifier.doi | 10.1016/j.laa.2021.10.006 | - |
dc.identifier.scopus | 2-s2.0-85117614228 | - |
dc.contributor.affiliation | Mathematics | en_US |
dc.relation.firstpage | 127 | - |
dc.relation.lastpage | 151 | - |
dc.relation.volume | 633 | - |
dc.description.rank | ~M21 | - |
item.grantfulltext | none | - |
item.cerifentitytype | Publications | - |
item.fulltext | No Fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | Article | - |
crisitem.author.orcid | 0000-0003-2908-305X | - |
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