Weighted Cages
G. Araujo-Pardo, C. De la Cruz, M. Matamala, M. A. Piza\~na

TL;DR
This paper introduces the concept of weighted cages, a new variant of regular graphs, providing existence criteria, order determinations for specific girths, Moore-like bounds, and computational insights.
Contribution
It defines weighted cages, characterizes their existence, and offers new bounds and computational results for these graph variants.
Findings
Existence criteria for weighted cages
Order determination for girths 3 and 4
Moore-like bounds established
Abstract
Cages (-regular graphs of girth 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 we determine their order; we give Moore-like bounds and present some computational results.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Combinatorial Mathematics · Interconnection Networks and Systems
