{"paper":{"title":"Spectra and energy of bipartite signed digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mushtaq A. Bhat, S. Pirzada","submitted_at":"2015-01-03T15:39:37Z","abstract_excerpt":"The set of distinct eigenvalues of a signed digraph $S$ together with their multiplicities is called its spectrum. The energy of a signed digraph $S$ with eigenvalues $z_1,z_2,\\cdots,z_n$ is defined as $E(S)=\\sum_{j=1}^{n}|\\Re z_j|$, where $\\Re z_j $ denotes real part of complex number $z_j$. In this paper, we show that the characteristic polynomial of a bipartite signed digraph of order $n$ with each cycle of length $\\equiv 0\\pmod 4$ negative and each cycle of length $\\equiv 2\\pmod 4$ positive is of the form \\\\ $$\\phi_S(z)=z^n+\\sum\\limits_{j=1}^{\\lfloor{\\frac{n}{2}}\\rfloor}(-1)^j c_{2j}(S)z^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00572","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"}