Analysis Of The Girth For Regular Bi-partite Graphs With Degree 3

TL;DR

This paper analyzes the enumeration-based search algorithm for finding regular bipartite graphs of degree 3, compares experimental results with existing literature, and confirms that the girth values align with known mathematical bounds.

Contribution

It provides a detailed description of the enumeration-based search algorithm and validates its effectiveness through experimental analysis against known bounds.

Findings

The girth values for (m, 3) BTUs are within known mathematical bounds.

Experimental results support the validity of the enumeration-based search algorithm.

The paper offers a detailed algorithmic description and comparative analysis.

Abstract

The goal of this paper is to derive the detailed description of the Enumeration Based Search Algorithm from the high level description provided in [16], analyze the experimental results from our implementation of the Enumeration Based Search Algorithm for finding a regular bi-partite graph of degree 3, and compare it with known results from the available literature. We show that the values of m for a given girth g for (m, 3) BTUs are within the known mathematical bounds for regular bi-partitite graphs from the available literature.