On ρ-labeling 2-regular graphs consisting of 5-cycles
نویسندگان
چکیده
Let G be a graph of size n with vertex set V (G) and edge set E(G). A ρ-labeling of G is a one-to-one function h : V (G) → {0, 1, . . . , 2n} such that {min{|h(u)−h(v)|, 2n+1−|h(u)−h(v)|} : {u, v} ∈ E(G)} = {1, 2, . . . , n}. Such a labeling of G yields a cyclic G-decomposition of K2n+1. It is conjectured by El-Zanati and Vanden Eynden that every 2-regular graph G admits a ρ-labeling. We show that the vertexdisjoint union of any number of 5-cycles admits a ρ-labeling.
منابع مشابه
Labelings of unions of up to four uniform cycles
We show that every 2-regular graph consisting of at most four uniform components has a ρ-labeling (or a more restricted labeling). This has an application in the cyclic decomposition of certain complete graphs into the disjoint unions of cycles.
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Let G be a graph of size n with vertex set V (G) and edge set E(G). A ρlabeling of G is a one-to-one function h : V (G) → {0, 1, . . . , 2n} such that {min{|h(u)−h(v)|, 2n+1−|h(u)−h(v)|} : {u, v} ∈ E(G)} = {1, 2, . . . , n}. Such a labeling of G yields a cyclicG-decomposition ofK2n+1. It is known that 2-regular bipartite graphs, the vertex-disjoint union of C3’s, and the vertex-disjoint union o...
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