A special case of completion invariance for the $c_2$ invariant of a graph

Abstract

The $c_2$ invariant is an arithmetic graph invariant defined by Schnetz. It is useful for understanding Feynman periods. Brown and Schnetz conjectured that the $c_2$ invariant has a particular symmetry known as completion invariance. This paper will prove completion invariance of the $c_2$ invariant in the case that $p=2$ and the completed graph has an odd number of vertices. The methods involve enumerating certain edge bipartitions of graphs; two different constructions are needed.

24 pages, edits according to referee comments

Cited by in corpus (1)

• Further investigations into the graph theory of ${\varphi }^4$-periods and the $c_2$ invariant