{"paper":{"title":"Randi\\'c Incidence Energy of Graphs","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":"2014-05-29T08:45:41Z","abstract_excerpt":"Let $G$ be a simple graph with vertex set $V(G) = \\{v_1, v_2,\\ldots, v_n\\}$ and edge set $E(G) = \\{e_1, e_2,\\ldots, e_m\\}$. Similar to the Randi\\'c matrix, here we introduce the Randi\\'c incidence matrix of a graph $G$, denoted by $I_R(G)$, which is defined as the $n\\times m$ matrix whose $(i, j)$-entry is $(d_i)^{-\\frac{1}{2}}$ if $v_i$ is incident to $e_j$ and $0$ otherwise. Naturally, the Randi\\'c incidence energy $I_RE$ of $G$ is the sum of the singular values of $I_R(G)$. We establish lower and upper bounds for the Randi\\'c incidence energy. Graphs for which these bounds are best possible"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7498","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"}