We consider the question of whether there is a converse to the Sunada Theorem in the context of -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 -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.
@article{AIF_1999__49_2_707_0, 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 = {https://aif.centre-mersenne.org/articles/10.5802/aif.1688/} }
TY - JOUR AU - Brooks, Robert TI - Non-Sunada graphs JO - Annales de l'Institut Fourier PY - 1999 SP - 707 EP - 725 VL - 49 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1688/ DO - 10.5802/aif.1688 LA - en ID - AIF_1999__49_2_707_0 ER -
Brooks, Robert. Non-Sunada graphs. Annales de l'Institut Fourier, Volume 49 (1999) no. 2, pp. 707-725. doi : 10.5802/aif.1688. https://aif.centre-mersenne.org/articles/10.5802/aif.1688/
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