Link Algebra: A new aproach to graph theory

TL;DR

This paper introduces Link Algebra, a new algebraic structure based on set theory, to formalize concepts in graph theory and provide alternative axiomatizations for various types of graphs.

Contribution

The paper develops Link Algebra, integrating set and antiset theory, and applies it to define graph concepts and alternative axiomatizations for complex graph types.

Findings

Link Algebra formalizes graph concepts like paths, cycles, and stars.

Provides alternative axiomatizations using multisets and ordered pairs.

Establishes a foundational algebraic framework for graph theory.

Abstract

In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once introduced Link Algebra, we will show the aplication on graph theory, like defining Paths, cycles and stars. Finally, we will se an alternative axiomatizations with Multisets and ordered pairs to algebraicaly define mutli, pseudo and oriented graphs.