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On prime labellings

✍ Scribed by Hung-Lin Fu; Kuo-Ching Huang

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 347 KB
Volume: 127
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)00477-9

No coin nor oath required. For personal study only.

✦ Synopsis

IS called a prime labelling if for each e = {u, u} in E, we have GCD(f(u),f(u))= 1. A graph admits a prime labelling is called a prime graph. Around ten years ago, Roger Entringer conjectured that every tree is prime. So far, this conjecture is still unsolved. In this paper, we show that the conjecture is true for trees of order up to 15, and also show that a few other classes of graphs are prime.

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