Mathematics

Conway–Gordon problem for reduced complete spatial graphs

Ph. G. Korablev^ab, A. A. Kazakov<sup>b

a</sup> Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences
^b Chelyabinsk State University

Abstract: This paper is devoted to $\mathrm{3D}$ embeddable graphs, which are obtained from full spatial graphs by removing several edges incident to one vertex. For all such graphs we introduce the analogue of Conway–Gordon function $\omega_2$. We prove that its value is zero for all spatial graphs obtained from full graphs with no less than eight vertices. There are examples of graphs with six vertices, where the value of this function is equal to unity.

Keywords: spatial graph; Hamiltonian cycle basis; link.

UDC: 515.162.8

Received: 04.03.2015

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