A problem on edgemagic labelings of cycles
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20140614Suggested citation
López Masip, SusanaClara;
Muntaner Batle, F. A.;
Rius Font, Miquel;
.
(2014)
.
A problem on edgemagic labelings of cycles.
Canadian Mathematical BulletinBulletin Canadien de Mathematiques, 2014, vol. 57, num. 2, p. 375380.
https://doi.org/10.4153/CMB20130361.
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Kotzig and Rosa defined in 1970 the concept of edgemagic labelings as follows: let G be a simple (p, q)graph (that is, a graph of order p and size q without loops or multiple edges). A bijective function f : V (G)∪E(G) → {1, 2, . . . , p + q} is an edgemagic labeling of G if f(u) + f(uv) + f(v) = k, for all uv ∈ E(G). A graph that admits an edgemagic labeling is called an edgemagic graph, and k is called the magic sum of the labeling. An old conjecture of Godbold and Slater sets that all possible theoretical magic sums are attained for each cycle of order n ≥ 7. Motivated by this conjecture, we prove that for all n0 ∈ N, there exists n ∈ N, such that the cycle Cn admits at least n0 edgemagic labelings with at least n0 mutually distinct magic sums. We do this by providing a lower bound for the number of magic sums of the cycle Cn, depending on the sum of the exponents of the odd primes appearing in the prime factorization of n.
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Canadian Mathematical BulletinBulletin Canadien de Mathematiques, 2014, vol. 57, num. 2, p. 375380European research projects
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