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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

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Volume 26, Issue 2


Distance between the spectra of graphs with respect to normalized Laplacian spectra

Mojgan Afkhami / Mehdi Hassankhani / Kazem Khashyarmanesh
  • Corresponding author
  • Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran
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Published Online: 2017-11-12 | DOI: https://doi.org/10.1515/gmj-2017-0051


Let Gn and Gn be two nonisomorphic graphs on n vertices with spectra (with respect to the adjacency matrix)


respectively. Define the distance between the spectra of Gn and Gn as

λ(Gn,Gn)=i=1n(λi-λi)2(or use i=1n|λi-λi|).

Define the cospectrality of Gn by

cs(Gn)=min{λ(Gn,Gn):Gn not isomorphic to Gn}.

In this paper, we investigate cs(Gn) for special classes of graphs with respect to normalized Laplacian spectra and we find cs(Kn), cs(nK1) and cs(K2+(n-2)K1) (n2). We also find an upper bound for csn.

Keywords: Spectra of graphs; measures on spectra of graphs

MSC 2010: 05C50; 05C31


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About the article

Received: 2015-05-27

Accepted: 2015-09-17

Published Online: 2017-11-12

Published in Print: 2019-06-01

Citation Information: Georgian Mathematical Journal, Volume 26, Issue 2, Pages 227–234, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2017-0051.

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