Cages (r-regular graphs of girth g and minimum order) and their variants have been studied for over seventy years. Here we propose a new variant, "weighted cages". We characterize their existence; for cases g=3,4 we determine their order; we give Moore-like bounds and present some computational results.
@article{arxiv.2411.02705,
title = {Weighted Cages},
author = {G. Araujo-Pardo and C. De la Cruz and M. Matamala and M. A. Pizaña},
journal= {arXiv preprint arXiv:2411.02705},
year = {2024}
}