In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting e...In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting essential maps on S2,N3 andN4 are given. In the same time, some known results can be derived.展开更多
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 Th...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.展开更多
文摘In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting essential maps on S2,N3 andN4 are given. In the same time, some known results can be derived.
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)
文摘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.
