科研之友
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摘要
An alpha-labeling of a bipartite graph Gamma of size e is an injective function f : V (Gamma) -> {0, 1, 2,..., e} such that {|f (x) - f (y) | : [x, y] is an element of E(Gamma)} = {1, 2,..., e} and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph P-8n,P-3 admits an alpha-labeling for any integer n >= 1 confirming that the conjecture posed by Vietri in [10] is true. In such a way we obtain an infinite class of decompositions of complete graphs into copies of P-8n,P-3.
- 出版日期2015
