In this paper, we introduce 'graph linear notation'—a complete graph invariant—as an alternative definition for finite graphs. This invariant is constructed using an algorithm similar to the one for finding canonical forms of graphs. Storing graph linear notation instead of a regular graph allows us to greatly simplify two major problems: constructing illustrations for graphs concerning possible graph symmetries and comparing two graphs for isomorphism. We also demonstrate the transferability to graph linear notations of classical graph theory concepts such as colorings and graph paths.
Blogger's Review: The introduction of graph linear notation offers a fresh perspective on the study of finite graphs, particularly in enhancing computational efficiency regarding symmetry and isomorphism. Its potential for practical applications is worth monitoring as it could significantly advance the field of graph theory.