A Moment-Based Method of Optinalysis

Abstract

Graph symmetry detection, similarity, and identity measures have been extensively studied in graph automorphism and isomorphism problems. Nevertheless, graph isomorphism and automorphism detection remain an open (unsolved) problem for many decades. In this paper, a new optinalytic coefficient termed as an optical moment coefficient was introduced for optinalysis. Its characteristic efficiency was tested for bijective property, invariance, deterministic polynomiality and non-polynomiality. The test results show that the new optical moment coefficient is very efficient for symmetry detections, similarity and identity measures between two isometric isomorphs and automorphs; and deterministic on polynomial and non-polynomial graph models.