On the number of representations of an element in a polygonal Cayley graph
Gabriella Kuhn, Paolo M. Soardi (1987)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We compute explicitly the number of paths of given length joining two vertices of the Cayley graph of the free product of cyclic groups of order k.