On the Prime Labeling of Generalized Petersen Graphs
نویسندگان
چکیده
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, . . . , |V | such that for every edge xy in E, 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 graphs P (n, 3) are not prime for odd n, prime for even n ≤ 100 and conjectured that P (n, 3) are prime for all even n. Mathematics Subject Classification: Primary 05C78; Secondary 52C30
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