English

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.

Keywords

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