Graphs with girth at least 5 with orders between 20 and 32
Alice Miller, Michael Codish

TL;DR
This paper investigates extremal graphs with girth at least 5 and orders between 20 and 32, determining degree bounds and embedded stars to facilitate classification of all non-isomorphic cases.
Contribution
It provides new properties and classifications of extremal graphs with girth 5 within a specific order range, including degree bounds and embedded star structures.
Findings
Identified possible minimum and maximum degrees for graphs with girth 5
Proved existence of embedded stars in certain cases
Enabled tractable search for all non-isomorphic graphs in the specified range
Abstract
We prove properties of extremal graphs of girth 5 and order 20 <=v <= 32. In each case we identify the possible minimum and maximum degrees, and in some cases prove the existence of (non-trivial) embedded stars. These proofs allow for tractable search for and identification of all non isomorphic cases.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Coding theory and cryptography
