Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2010-11-01

Journal: UTILITAS MATHEMATICA

Included Journals: Scopus、SCIE

Volume: 83

Page Number: 95-106

ISSN: 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.