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Proyecciones (Antofagasta)

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Abstract

JEYANTHI, P.; PHILO, S.  and  YOUSSEF, Maged Z.. Odd harmonious labeling of grid graphs. Proyecciones (Antofagasta) [online]. 2019, vol.38, n.3, pp.411-429. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-2019-03-0027.

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.

Keywords : Harmonious labeling; Odd harmonious labeling; Grid graph; Path union of graphs; One point union of path of graphs; t-super subdivision of graphs; 05C78.

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