c₂ Invariants of Recursive Families of Graphs

2017/01/05 by Chorney, Wesley, Yeats, Karen
#05C25 #05C31 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1701.01208

Abstract

The c₂ invariant, defined by Schnetz in 2011, is an arithmetic graph invariant created towards a better understanding of Feynman integrals. This paper looks at some graph families of interest, with a focus on decompleted toroidal grids. Specifically, the c₂ invariant for p=2 is shown to be zero for all decompleted non-skew toroidal grids. We also calculate the c₂ invariant at p=2 for G a family of graphs called X-ladders. Finally, we show these methods can be applied to any graph with a recursive structure, for any fixed p.

Related

• A few c₂ invariants of circulant graphs
• Properties of c₂ invariants of Feynman graphs
• A study on prefixes of c₂ invariants
• A special case of completion invariance for the c₂ invariant of a graph
• Completing the c₂ completion conjecture for p=2