{"paper":{"title":"Minimal Skew energy of oriented bicyclic graphs with a given diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ligong Wang, Xiangxiang Liu","submitted_at":"2016-10-21T01:50:44Z","abstract_excerpt":"Let $S(G^{\\sigma})$ be the skew-adjacency matrix of the oriented graph $G^{\\sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $\\sigma$ to each of its edges. The skew energy of an oriented graph $G^{\\sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{\\sigma})$. For any positive integer $d$ with $3\\leq d\\leq n-3$, we determine the graph with minimal skew energy among all oriented bicyclic graphs that contain no vertex disjoint odd cycle of lengths $s$ and $l$ with $s+l\\equiv 2(mod 4)$ on $n$ vertices with a given diameter $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06644","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":""},"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"}