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Supermagic Complete Graphs

Published online by Cambridge University Press:  20 November 2018

B. M. Stewart
B. M. Stewart*
Affiliation:
Michigan State University
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In our paper “Magic graphs” (1) we showed that every complete graph Kn with n ⩾ 5 is “magic,” i.e., if the vertex set is indicated {vi} and if eij is the edge joining vi and vj, i ≠ j , then there exists a function α(eij) such that the set {α(eij)} consists of distinct positive rational integers and the vertex sums

1

have a constant value σ(α) for k = 1, 2, … , n. We noted that K2 is magic and showed that K3 and K4 are not magic.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 427 - 438
Copyright
Copyright © Canadian Mathematical Society 1967

References

Stewart, B. M., Magic graphs, Can. J. Math., 18 (1966), 1031–1059.Google Scholar