{"paper":{"title":"Spectral properties of the Cayley Graphs of split metacyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kashyap Rajeevsarathy, Pawan Kumar Aurora, Siddhartha Sarkar, S. Lakshmivarahan","submitted_at":"2016-09-20T05:28:52Z","abstract_excerpt":"Let $\\Gamma(G,S)$ denote the Cayley graph of a group $G$ with respect to a set $S \\subset G$. In this paper, we analyze the spectral properties of the Cayley graphs $\\mathcal{T}_{m,n,k} = \\Gamma(\\mathbb{Z}_m \\ltimes_k \\mathbb{Z}_n, \\{(\\pm 1,0),(0,\\pm 1)\\})$, where $m,n \\geq 3$ and $k^m \\equiv 1 \\pmod{n}$. We show that the adjacency matrix of $\\mathcal{T}_{m,n,k}$, upto relabeling, is a block circulant matrix, and we also obtain an explicit description of these blocks. By extending a result due to Walker-Mieghem to Hermitian matrices, we show that $\\mathcal{T}_{m,n,k}$ is not Ramanujan, when ei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06022","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}