Enumerating super edge-magic labelings for the union of nonisomorphic graphs

Ahmad, Ali; López Masip, Susana-Clara; Muntaner Batle, F. A.; Rius Font, Miquel

doi:https://doi.org/10.1017/S0004972711002292

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Issue date

2011

Author

Ahmad, Ali

López Masip, Susana-Clara

Muntaner Batle, F. A.

Rius Font, Miquel

Suggested citation

Ahmad, Ali; López Masip, Susana-Clara; Muntaner Batle, F. A.; Rius Font, Miquel; . (2011) . Enumerating super edge-magic labelings for the union of nonisomorphic graphs. Bulletin of the Australian Mathematical Society, 2011, vol. 84, num. 2, p. 310-321. https://doi.org/10.1017/S0004972711002292.

Abstract

A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:V ∪E→{i}p+qi=1 such that: (1) f(u)+f(uv)+f(v)=k for all uv∈E; and (2) f(V )={i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if

uv∈E(G) , u′,v′ ∈V (G) and dG (u,u′ )=dG (v,v′ )<+∞, then f(u)+f(v)=f(u′ )+f(v′ ). In this paper we introduce the concept of strong super edge-magic labeling of a graph G with respect to a linear forest F, and we study the super edge-magicness of an odd union of nonnecessarily isomorphic acyclic graphs. Furthermore, we find exponential lower bounds for the number of super edge-magic labelings of these unions. The case when G is not acyclic will be also considered.

URI

http://hdl.handle.net/10459.1/66072

DOI

https://doi.org/10.1017/S0004972711002292

Is part of

Bulletin of the Australian Mathematical Society, 2011, vol. 84, num. 2, p. 310-321