{"paper":{"title":"Forwarding and optical indices of 4-regular circulant networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hamid Mokhtar, Heng-Soon Gan, Sanming Zhou","submitted_at":"2014-05-27T09:36:55Z","abstract_excerpt":"An all-to-all routing in a graph $G$ is a set of oriented paths of $G$, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing $R$ is the number of times it is used (in either direction) by paths of $R$, and the maximum load of an edge is denoted by $\\pi(G,R)$. The edge-forwarding index $\\pi(G)$ is the minimum of $\\pi(G,R)$ over all possible all-to-all routings $R$, and the arc-forwarding index $\\overrightarrow{\\pi}(G)$ is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6848","kind":"arxiv","version":2},"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"}