Non-Sunada graphs
Annales de l'Institut Fourier, Volume 49 (1999) no. 2, pp. 707-725.

We consider the question of whether there is a converse to the Sunada Theorem in the context of k-regular graphs. We give a weak converse to the Sunada Theorem, which gives a necessary and sufficient condition for two graphs to be isospectral in terms of a Sunada-like condition, and show by example that a strong converse does not hold.

Nous considérons la question de l’existence d’une réciproque du théorème de Sunada dans le cadre des graphes k-réguliers. Nous étudions une réciproque faible du théorème de Sunada qui donne une condition nécessaire et suffisante pour que deux graphes soient isospectraux, en termes d’une condition “presque-Sunada”, et proposons un contre-exemple qui montre qu’il n’y a pas de réciproque forte.

     author = {Brooks, Robert},
     title = {Non-Sunada graphs},
     journal = {Annales de l'Institut Fourier},
     pages = {707--725},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {49},
     number = {2},
     year = {1999},
     doi = {10.5802/aif.1688},
     zbl = {0926.58021},
     mrnumber = {2000i:58062},
     language = {en},
     url = {}
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Brooks, Robert. Non-Sunada graphs. Annales de l'Institut Fourier, Volume 49 (1999) no. 2, pp. 707-725. doi : 10.5802/aif.1688.

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