{"paper":{"title":"A Comprehensive Study of Clique Graphs and Clique Regular Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Connor Phillips","submitted_at":"2026-05-19T20:49:26Z","abstract_excerpt":"If $\\Gamma$ is a graph for which every edge is in exactly one clique of order $\\omega$, then one can form a new graph with vertex set equal to these cliques. This is a generalization of the line graph of $\\Gamma$. We discover many general results and classifications related to these clique graphs that will be useful to researchers studying graphs with this property. In particular, we find bounds on the spectrum of $\\Gamma$ (with exact results when $\\Gamma$ is $k$-regular) and some complete classifications when $\\Gamma$ is strongly regular. We apply our results to derive novel information about"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22867","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/2605.22867/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"}