Generation of anti-magic graphs from binary graph products
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Ragukumar, P. [1]
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[1] Vellore Institute of Technology.
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- Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 3, 2023, págs. 651-661
- Idioma: inglés
- DOI: 10.22199/issn.0717-6279-5220
- Enlaces
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Resumen
An anti-magic labeling of a graph G is a one-to-one correspondence between E(G) and {1, 2, ··· , |E|} such that the vertex-sum for distinct vertices are different. Vertex-sum of a vertex u ∈ V (G) is the sum of labels assigned to edges incident to the vertex u. It was conjectured by Hartsfield and Ringel that every tree other than K2 has an anti-magic labeling. In this paper, we consider various binary graph products such as corona, edge corona and rooted products to generate anti-magic graphs. We prove that corona products of an anti-magic regular graph G with K1 and K2 are anti-magic. Further, we prove that rooted product of two anti-magic trees are anti-magic. Also, we prove that rooted product of an anti-magic graph with an anti-magic tree admits anti-magic labeling.
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