Graphs with girth at least 5 with orders between 20 and 32

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.