Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Optinalysis: Isometric Isomorphism and Automorphism Through A Looking-Glass

Version 1 : Received: 3 August 2020 / Approved: 5 August 2020 / Online: 5 August 2020 (03:43:11 CEST)

How to cite: Abdullahi, K.B. Optinalysis: Isometric Isomorphism and Automorphism Through A Looking-Glass. Preprints 2020, 2020080072 (doi: 10.20944/preprints202008.0072.v1). Abdullahi, K.B. Optinalysis: Isometric Isomorphism and Automorphism Through A Looking-Glass. Preprints 2020, 2020080072 (doi: 10.20944/preprints202008.0072.v1).

## Abstract

Measures of graph symmetry, similarity, and identity have been extensively studied in graph automorphism and isomorphism detection problems. Nevertheless, graph isomorphism detection remains an open (unsolved) problem for many decades. In this paper, a new and efficient methodological paradigm, called optinalysis, is proposed for symmetry detections, similarity, and identity measures between isometric isomorphs or automorphs. Optinalysis is explained and expressed in clearly stated definitions and prove theorems, which conform to the definitions and theorems of isometry, isomorphism, and automorphism. Analogous to the polynomiality formalization for an efficient algorithm for graph isomorphism detection, optinalysis is however deterministic on polynomial and non-polynomial graph models.

## Subject Areas

Automorphism; Identity; Isometry; Isomorphism; Similarity; Symmetry.

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