Conway–Gordon Problem for Reduced Complete Spatial Graphs
Authors
Philipp Glebovich Korablev
Chelyabinsk State University; Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences
Alexander Andreevich Kazakov
Chelyabinsk State University
Keywords:
spatial graph, Hamiltonian cycle basis, link
Abstract
This paper is devoted to 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 ω2. 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.
Author Biographies
Philipp Glebovich Korablev, Chelyabinsk State University; Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences
Associate Professor, Department of Computer Topology and Algebra, Laboratory of Quantum Topology, Chelyabinsk State University; Head of Mathematician of Algorithmic Topology Department, Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences
Alexander Andreevich Kazakov, Chelyabinsk State University
Lecturer, Department of Computer Topology and Algebra
