Enumeration Based Search Algorithm For Finding A Regular Bi-partite Graph Of Maximum Attainable Girth For Specified Degree And Number Of Vertices

TL;DR

This paper develops an enumeration search algorithm to find regular bipartite graphs with maximum girth for given degree and vertices, leveraging mathematical constraints to optimize the search process.

Contribution

It introduces a novel enumeration algorithm for maximum girth regular bipartite graphs using rigorous mathematical restrictions and analyzes its structure and complexity.

Findings

Algorithm effectively finds maximum girth graphs for specified parameters.

Mathematical restrictions significantly reduce the search space.

Analysis of the algorithm's computational complexity.

Abstract

We introduce a search problem for finding a regular bi-partite graph of maximum attainable girth for specified degree and number of vertices, by restricting the search space using a series of mathematically rigourous arguments from [1] and [2]. The goal of this paper is to derive the enumeration search algorithm for finding a girth maximum (m, r) BTU, which is notation for regular partite graph that has been introduced in [1], using the optimal partition results from [2] as a starting point, and also understand the structure of the search space and the computational complexity of the algorithm.