On Conway-Gordon type theorems for graphs in the Petersen family

Hiroka Hashimoto; Ryo Nikkuni

doi:10.1142/s021821651350048x

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arXiv · 1209.2006

On Conway-Gordon type theorems for graphs in the Petersen family

Hiroka Hashimoto·Ryo Nikkuni

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Abstract

For every spatial embedding of each graph in the Petersen family, it is known that the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2. In this paper, we give an integral lift of this formula in terms of the square of the linking number and the second coefficient of the Conway polynomial.

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Hiroka Hashimoto, Ryo Nikkuni. 2012-09-10. On Conway-Gordon type theorems for graphs in the Petersen family. https://doi.org/10.1142/s021821651350048x

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