科研之友
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摘要
For each k, 1 <= k <= n, we construct a dot product of n copies of the Petersen graph whose orientable genus is precisely k. We show that these are all possible values for the genus of P-n. This result gives counterexamples of all possible genera to a conjecture of Tinsley and Watkins from 1982. We show that the Petersen graph is the only Petersen power which can be embedded into the projective plane. For each k, 2 <= k <= n-1, we construct a Petersen power P-n whose non-orientable genus is precisely k.
- 出版日期2011-5
