On Conway-Gordon type theorems for graphs in the Petersen family
  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. 
Hiroka Hashimoto and Ryo Nikkuni
math.GT