{"paper":{"title":"Resistance distance and Kirchhoff index in the corona-vertex and the corona $-$ edge of subdivision graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jia-Bao Liu, Masoud Karimi, Qun Liu, Shaohui Wang","submitted_at":"2016-11-14T01:18:34Z","abstract_excerpt":"The subdivision graph $S(G)$ of a graph $G$ is the graph obtained by inserting a new vertex into every edge of $G$. In $\\cite{PL}$, two classes of new corona graphs, the corona-vertex of the subdivision graph $G_{1}\\diamondsuit G_{2}$ and corona-edge of the subdivision graph $G_{1}\\star G_{2}$ were defined. The adjacency spectrum and the signless Laplacian spectrum of the two new graphs were computed when $G_{1}$ is an arbitrary graph and $G_{2}$ is an $r$-regular graph. In this paper, we give the formulate of the resistance distance and the Kirchhoff index in $G_{1}\\diamondsuit G_{2}$ and $G_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04219","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"}