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On Two Conjectures About Set-graceful Graphs

✍ Scribed by Mollard, M.; Payan, C.

Book ID
122414814
Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
211 KB
Volume
10
Category
Article
ISSN
0195-6698

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πŸ“œ SIMILAR VOLUMES

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We give graceful numberings to the following graphs: (a) the union of n K4 having one edge in common, in other words the join of K2 and the union of n disjoint K2 and (b) the union of n C4 having one edge in common, in other words the product of K2 and K,,", with n + l not a multiple of 4.

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A positive integer m is said to be a practical number if every integer n, with 1 n \_(m), is a sum of distinct positive divisors of m. In this note we prove two conjectures of Margenstern: (i) every even positive integer is a sum of two practical numbers; (ii) there exist infinitely many practical