2-regular Digraphs of the Lovelock Lagrangian
General Mathematics
2023-02-28 v3
Abstract
The manuscripts tabulates arc lists of the 1, 1, 3, 8, 25, 85, 397 ... unlabeled 2-regular digraphs on n=0, 1, 2, ..., 9 nodes, including disconnected graphs, graphs with multiarcs and/or graphs with loops. Each of these graphs represents one term of the Lagrangian of Lovelock's type -- a contraction of a product of n Riemann tensors -- once the 2 covariant and 2 contravariant indices of a tensor are associated with the in-edges and out-edges of a node.
Cite
@article{arxiv.1903.12477,
title = {2-regular Digraphs of the Lovelock Lagrangian},
author = {Richard J. Mathar},
journal= {arXiv preprint arXiv:1903.12477},
year = {2023}
}
Comments
Version 3: enumerations of fairly 2-regular digraphs and Java source code added