摘要
In the paper, we prove that for every integer n ≥ 1, there exists a Petersen power pn with nonorientable genus and Euler genus precisely n, which improves the upper bound of Mohar and Vodopivec＇s result [J. Graph Theory, 67, 1-8 （2011）] that for every integer k （2 ≤ k ≤ n- 1）, a Petersen power Pn exists with nonorientable genus and Euler genus precisely k.
In the paper, we prove that for every integer n ≥ 1, there exists a Petersen power pn with nonorientable genus and Euler genus precisely n, which improves the upper bound of Mohar and Vodopivec＇s result [J. Graph Theory, 67, 1-8 （2011）] that for every integer k （2 ≤ k ≤ n- 1）, a Petersen power Pn exists with nonorientable genus and Euler genus precisely k.
基金
supported by the Fundamental Research Funds for the Central Universities(Grand No.NZ2015106)
supported by National Natural Science Foundation of China(Grant Nos.11471106 and 11371133)
NSFC of Hu’nan(Grant No.14JJ2043)
