Odd harmonious labeling of grid graphs
Abstract A graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function f* : E(G) → {1, 3, · · · , 2q − 1} defined by f∗ (uv) = f (u) + f (v) is a bijection. In this pa...
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| Autores principales: | , , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2019
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300411 |
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| Sumario: | Abstract A graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function f* : E(G) → {1, 3, · · · , 2q − 1} defined by f∗ (uv) = f (u) + f (v) is a bijection. In this paper we prove that path union of t copies of Pm×Pn, path union of t different copies of Pmᵢ×Pnᵢ where 1 ≤ i ≤ t, vertex union of t copies of Pm×Pn, vertex union of t different copies of Pmᵢ×Pnᵢ where 1 ≤ i ≤ t, one point union of path of Ptn (t.n.Pm×Pm), t super subdivision of grid graph Pm×Pn are odd harmonious graphs. |
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