Matrix algorithm for determination of the elementary paths and elementary circuits using exotic semirings

TL;DR

This paper introduces a novel matrix-based algorithm leveraging exotic semirings to efficiently identify elementary paths, circuits, and Hamiltonian paths in directed graphs, enhancing graph analysis capabilities.

Contribution

The paper presents a new matrix algorithm utilizing exotic semirings for determining elementary paths and circuits, including Hamiltonian paths, in directed graphs.

Findings

Effective enumeration of elementary paths and circuits.

Successful application to Hamiltonian path problems.

Potential for improved graph analysis algorithms.

Abstract

We propose a new method for determining the elementary paths and elementary circuits in a directed graph. Also, the Hamiltonian paths and Hamiltonian circuits are enumerated.