{"paper":{"title":"Maximum nullity and zero forcing number on cubic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ebrahim Vatandoost, Saieed Akbari, Yasser Golkhandy Pour","submitted_at":"2017-05-27T06:32:00Z","abstract_excerpt":"Let $G$ be a graph. The maximum nullity of $G$, denoted by $M(G)$, is defined to be the largest possible nullity over all real symmetric matrices $A$ whose $a_{ij}\\neq 0$ for $i\\neq j$, whenever two vertices $u_i$ and $u_j$ of $G$ are adjacent. In this paper, we characterize all cubic graphs with zero forcing number $3$. As a corollary, it is shown that if the zero forcing number is $3$, then $M(G)=3$. In addition, we introduce a family of cubic graphs containing graphs $G$ with $M(G)=Z(G)=4$.\nAlso, we provide an algorithm which make a relation between maximum nullity of $G$ and the number of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09773","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"}