{"paper":{"title":"Bounds for Different Spreads of Line and Total Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.SP","authors_text":"E. Andrade, E. Lenes, E. Mallea, Jonnathan Rodr\\'iguez, M. Robbiano","submitted_at":"2018-07-08T23:49:14Z","abstract_excerpt":"In this paper we explore some results concerning the spread of the line and the total graph of a given graph. In particular, it is proved that for an $(n,m)$ connected graph $G$ with $m > n \\geq 4$ the spread of $G$ is less than or equal to the spread of its line graph, where the equality holds if and only if $G$ is regular bipartite. A sufficient condition for the spread of the graph not be greater than the signless Laplacian spread for a class of non bipartite and non regular graphs is proved. Additionally, we derive an upper bound for the spread of the line graph of graphs on $n$ vertices h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02899","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"}