Abstract:We introduce a switching operation, inspired by the Godsil-McKay switching, in order to obtain pairs of G-cospectral gain graphs, that are gain graphs cospectral with respect to every representation of the gain group G. For instance, for two signed graphs, this notion of cospectrality is equivalent to the cospectrality of their signed adjacency matrices together with the cospectrality of their underlying graphs. Moreover, we introduce another more flexible switching in order to obtain pairs of gain graphs cosp… Show more
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