Nonorientable Genera of Petersen Powers

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 ex...

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Published inActa mathematica Sinica. English series Vol. 31; no. 4; pp. 557 - 564
Main Authors Liu, Wen Zhong, Shen, Ting Ru, Chen, Yi Chao
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.04.2015
Springer Nature B.V
Subjects
Eulers equations
Graph theory
Integers
Mathematical analysis
Mathematics
Mathematics and Statistics
Studies
Upper bounds
功率
图论
整数
欧拉
消弧线
05C10
Dot product
genus
Petersen power
05C15
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Summary: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.
Bibliography:Dot product, Petersen power, genus
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.
11-2039/O1
ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-4096-9