Geodesic
Graph cospectrality using neighborhood matrices
The electronic journal of combinatorics, Tome 19 (2012) no. 3

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Zbl
In this note we address the problem of graph isomorphism by means of eigenvalue spectra of different matrix representations: the neighborhood matrix $\hat{M}$, its corresponding signless Laplacian $Q_{\hat{M}}$, and the set of higher order adjacency matrices $M_{\ell}$s. We find that, in relation to graphs with at most 10 vertices, $Q_{\hat{M}}$ leads to better results than the signless Laplacian $Q$; besides, when combined with $\hat{M}$, it even surpasses the Godsil and McKay switching method.
DOI : 10.37236/2617
Classification : 05C30, 05C50, 05C60, 05C22
Mots-clés : cospectrality, neighborhood

Aline Duarte Bessa  1   ; Ivan Carmo Rocha-Neto  1   ; Suani Tavares Rubim de Pinho  1   ; Roberto Fernandes Silva Andrade  1   ; Thierry Correa Petit Lobao  1

1 Universidade Federal da Bahia 
Aline Duarte Bessa; Ivan Carmo Rocha-Neto; Suani Tavares Rubim de Pinho; Roberto Fernandes Silva Andrade; Thierry Correa Petit Lobao. Graph cospectrality using neighborhood matrices. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2617
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     author = {Aline Duarte Bessa and Ivan Carmo Rocha-Neto and Suani Tavares Rubim de Pinho and Roberto Fernandes Silva Andrade and Thierry Correa Petit Lobao},
     title = {Graph cospectrality using neighborhood matrices},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {3},
     doi = {10.37236/2617},
     zbl = {1252.05085},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2617/}
}
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