On the power of a perturbation for testing non-isomorphism of graphs |
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Authors: | G M Prabhu Narsingh Deo |
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Institution: | (1) Computer Science Department, Iowa State University, 50011 Ames, Iowa, USA;(2) Computer Science Department, Washington State University, 99164-1210 Pullman, Washington, USA |
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Abstract: | In this paper we prove an inverted version of A. J. Schwenk's result, which in turn is related to Ulam's reconstruction conjecture. Instead of deleting vertices from an undirected graphG, we add a new vertexv and join it to all other vertices ofG to get a perturbed graphG+v. We derive an expression for the characteristic polynomial of the perturbed graphG+v in terms of the characteristic polynomial of the original graphG. We then show the extent to which the characteristic polynomials of the perturbed graphs can be used in determining whether two graphs are non-isomorphic.This work was supported by the U.S. Army Research Office under Grant DAAG29-82-K-0107. |
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Keywords: | Non-isomorphism of graphs characteristic polynomial reconstruction conjecture graph perturbation |
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