{"paper":{"title":"On the structure and spectra of an induced subgraph of essential ideal graph of $\\mathbb{Z}_{n}$","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CO","math.RA"],"primary_cat":"math.AC","authors_text":"A.V. Chithra, P. Jamsheena","submitted_at":"2023-10-17T05:03:57Z","abstract_excerpt":"Let $R$ be a commutative ring with unity. The essential ideal graph $\\mathcal{E}_R$ of $R$ is a graph in which the vertex set comprises of set of all nonzero proper ideals of $R$ and two vertices $I$ and $K$ are adjacent if and only if $I+K$ is an essential ideal. In this paper, we discuss the structure of an induced subgraph of the essential ideal graph of the ring $\\mathbb{Z}_{n}$ as a $\\mathscr{G}$-generalized join graph and thereby completely determine the structure of $\\mathcal{E}_{\\mathbb{Z}_{n}}$. Also, we prove a characterization of $\\mathcal{E}_{\\mathbb{Z}_{n}}$ to be Laplacian integr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.10999","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.10999/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}