On c2 invariants of some 4-regular Feynman graphs

Abstract

The obstruction for application of techniques like denominator reduction for the computation of the c2 invariant of Feynman graphs in general is the absence of a 3-valent vertex. In this paper such a formula for a 4-valent vertex is derived. The formula allows us to compute the c 2 invariant of new graphs, for instance, some 4-regular graphs with small loop number.