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2021•Preprints.orgOpen access

A Polynomial Time Algorithm for Graph Isomorphism and Automorphism

Sardar Anisul Haque

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Abstract

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.

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What this paper is about

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.

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Available abstract

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.

Key concepts: Graph automorphism, Graph isomorphism, Automorphism, Time complexity, Isomorphism (crystallography), Mathematics, Combinatorics, Discrete mathematics

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