A Polynomial Invariant Of Twisted Graph Diagrams

TL;DR

This paper introduces a polynomial invariant for twisted graph diagrams, establishing a connection with virtual graph diagrams and providing a lower bound for their virtual crossing number.

Contribution

It develops a Yamada-type polynomial invariant specifically for twisted graph diagrams, linking abstract and twisted diagrams.

Findings

Polynomial invariant offers a lower bound for virtual crossing number.

Bijection between abstract and twisted graph diagrams established.

Invariant extends Yamada-type polynomials to twisted graphs.

Abstract

Twisted graph diagrams are virtual graph diagrams with bars on edges. A bijection between abstract graph diagrams and twisted graph diagrams is constructed. Then a polynomial invariant of Yamada-type is developed which provides a lower bound for the virtual crossing number of virtual graph diagrams.