{"paper":{"title":"On fixing sets of composition and corona product of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"I. Irshad, I. Javaid, M. S. Aasi, M. Salman","submitted_at":"2015-07-08T07:46:02Z","abstract_excerpt":"A fixing set $\\mathcal{F}$ of a graph $G$ is a set of those vertices of the graph $G$ which when assigned distinct labels removes all the automorphisms from the graph except the trivial one. The fixing number of a graph $G$, denoted by $fix(G)$, is the smallest cardinality of a fixing set of $G$. In this paper, we study the fixing number of composition product, $G_1[G_2]$ and corona product, $G_1 \\odot G_2$ of two graphs $G_1$ and $G_2$ with orders $m$ and $n$ respectively. We show that for a connected graph $G_1$ and an arbitrary graph $G_2$ having $l\\geq 1$ components $G_2^1$, $G_2^2$, ... $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02053","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"}