Knotting and linking in the Petersen family

Abstract

This paper focuses on the graphs in the Petersen family, the set of minor minimal intrinsically linked graphs. We prove there is a relationship between algebraic linking of an embedding and knotting in an embedding. We also present a more explicit relationship for the graph $K_{3,3,1}$ between knotting and linking, which relates the sum of the squares of linking numbers of links in the embedding and the second coefficient of the Conway polynomial of particular cycles in the embedding.