{"paper":{"title":"Total Irregularity and $f_t$-Irregularity of Linear Jaco Graphs$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johan Kok","submitted_at":"2014-06-24T08:40:21Z","abstract_excerpt":"Total irregularity of a simple undirected graph $G$ is defined to be $irr_t(G) = \\frac{1}{2}\\sum\\limits_{u, v \\in V(G)}|d(u) - d(v)|$. See Abdo and Dimitrov [2]. We allocate the \\emph{Fibonacci weight,} $f_i$ to a vertex $v_j$ of a simple connected graph, if and only if $d(v_j) = i$ and define the \\emph{total fibonaccian irregularity} or $f_t-irregularity$ denoted $firr_t(G)$ for brevity, as: $firr_t(G) = \\sum\\limits_{i=1}^{n-1}\\sum\\limits_{j=i+1}^{n}|f_i - f_j|.$ The concept of an \\emph{edge-joint} is also introduced to be the simple undirected graph obtained from two simple undirected graphs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6168","kind":"arxiv","version":3},"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"}