{"paper":{"title":"On the construction of l-equienergetic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hilal A Ganie, S. Pirzada","submitted_at":"2013-10-12T17:10:55Z","abstract_excerpt":"For a graph with $n$ vertices and $m$ edges, having Laplacian spectrum $\\mu_1, \\mu_2, \\cdots,\\mu_n$ and signless Laplacian spectrum $\\mu^+_1,\\mu^+_2, \\cdots,\\mu^+_n$, the Laplacian energy and signless Laplacian energy of $G$ are respectively, defined as $LE(G)=\\sum_{i=1}^{n}|\\mu_i-\\frac{2m}{n}|$ and $LE^+(G)=\\sum_{i=1}^{n}|\\mu^+_i-\\frac{2m}{n}|$. Two graphs $G_1$ and $G_2$ of same order are said to be $L$-equienergetic if $LE(G_1)=LE(G_2)$ and $Q$-equienergetic if $LE^{+}(G_1)=LE^{+}(G_2)$. The problem of constructing graphs having same Laplacian energy has been considered by Stevanovic for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3406","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"}