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Indexed by:期刊论文

Date of Publication:2010-11-01

Journal:UTILITAS MATHEMATICA

Included Journals:SCIE、Scopus

Volume:83

Page Number:95-106

ISSN No.:0315-3681

Key Words:Prime labeling; Prime graph; Generalized Petersen graph

Abstract:A graph G with vertex set V is said to have a prime labeling if its vertices can be labeled with distinct integers 1,2, ... , vertical bar V vertical bar such that for every edge xy in G, the labels assigned to x and y are relatively prime or coprime. A graph is called prime if it has a prime labeling. In this paper, we show that generalized Petersen graph P(n, 1) is not prime for odd n, prime for even n <= 2500, and conjecture that P(n, 1) is prime for all even n.