An alternative way of defining finite graphs

Computer Science > Discrete Mathematics [Submitted on 16 Jun 2026] Title:An alternative way of defining finite graphs View PDF HTML (experimental)Abstract:In this paper we introduce "graph linear notation" -- a complete graph invariant -- which is positioned as an alternative definition for the finite graphs. This invariant is constructed using an algorithm similar to the algorithm of finding canonical forms of graphs. Storing graph linear notation instead of a regular graph allows us to greatly simplify two major problems: the construction of illustrations for graphs with regards to possible graph symmetries, and the comparison of two graphs for isomorphism. We also demonstrate the transferability to the graph linear notations such classical graph theory concepts as colourings and graph paths. Current browse context: cs.DM References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.