{"paper":{"title":"The Laplacian polynomial of graphs derived from regular graphs and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fu-Tao Hu, Jia-Bao Liu, Xiang-Feng Pan","submitted_at":"2014-11-20T11:43:19Z","abstract_excerpt":"Let $R(G)$ be the graph obtained from $G$ by adding a new vertex corresponding to each edge of $G$ and by joining each new vertex to the end vertices of the corresponding edge. Let $RT(G)$ be the graph obtained from $R(G)$ by adding a new edge corresponding to every vertex of $G$, and by joining each new edge to every vertex of $G$. In this paper, we determine the Laplacian polynomials of $RT(G)$ of a regular graph $G$. Moreover, we derive formulae and lower bounds of Kirchhoff index of the graphs. Finally we also present the formulae for calculating the Kirchhoff index of some special graphs "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5509","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"}