Author(s)

Jiaming Dong^*, Huilan Li^*#

School of Mathematics and Statistics, Shandong Normal University, Jinan, China.

A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the unshuffle coproduct. In fact, it is a Hopf algebra since it is graded connected. The main conclusions are that the vector space spanned by labeled simple graphs arising from the unshuffle coproduct is a Hopf algebra and that there is a Hopf homomorphism from permutations to label simple graphs.

Hopf Algebra, Labeled Simple Graph, Conjunction Product, Unshuffle Coproduct, Compatibility

Dong, J. and Li, H. (2023) Hopf Algebra of Labeled Simple Graphs. Open Journal of Applied Sciences, 13, 120-135. doi: 10.4236/ojapps.2023.131011.