Hopf algebra of labeled simple graphs arising from super-shuffle product

Abstract

From the connections between permutations and labeled simple graphs, we generalized the super-shuffle product and the cut-box coproduct on permutations to labeled simple graphs. We then proved that the vector space spanned by labeled simple graphs is a Hopf algebra with these two operations.

Keywords

• hopf algebra
• labeled simple graph
• super-shuffle product
• cut-box coproduct