Magic and Antimagic Graphs by Martin Bača & Mirka Miller & Joe Ryan & Andrea Semaničová-Feňovčíková

Author:Martin Bača & Mirka Miller & Joe Ryan & Andrea Semaničová-Feňovčíková
Language: eng
Format: epub
ISBN: 9783030245825
Publisher: Springer International Publishing

Notice that, since p is odd, this gives at the same time an (a, r)-VAE labeling of F 1. We label the edges of F 2 as

for every i = 1, 2, …, p and

for every j = 3, 4, …, r and i = 1, 2, …, p. It is easy to see that the set of the edge labels in each factor F j is

(5.1)

Thus, α is a bijection E(G) →{1, 2, …, pr}. The vertex-weight of vertex v i, i = 1, 2, …, p, in α is

Using (5.1), we observe that

Thus, the vertex-weights w α(v i) form the set

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