{"paper":{"title":"Skew Randi\\'c Matrix and Skew Randi\\'c Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fei Huang, Ran Gu, Xueliang Li","submitted_at":"2014-06-05T09:02:35Z","abstract_excerpt":"Let $G$ be a simple graph with an orientation $\\sigma$, which assigns to each edge a direction so that $G^\\sigma$ becomes a directed graph. $G$ is said to be the underlying graph of the directed graph $G^\\sigma$. In this paper, we define a weighted skew adjacency matrix with Rand\\'c weight, the skew Randi\\'c matrix ${\\bf R_S}(G^\\sigma)$, of $G^\\sigma$ as the real skew symmetric matrix $[(r_s)_{ij}]$ where $(r_s)_{ij} = (d_id_j)^{-\\frac{1}{2}}$ and $(r_s)_{ji} = -(d_id_j)^{-\\frac{1}{2}}$ if $v_i \\rightarrow v_j$ is an arc of $G^\\sigma$, otherwise $(r_s)_{ij} = (r_s)_{ji} = 0$. We derive some pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1300","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"}