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Walks on unitary Cayley graphs and applications

E Cancela, DA Jaume, A Pastine, D Videla - arXiv preprint arXiv …, 2012 - arxiv.org
E Cancela, DA Jaume, A Pastine, D Videla
arXiv preprint arXiv:1203.2473, 2012•arxiv.org
In this paper, we determine an explicit formula for the number of walks in $ X_n=\textsf
{Cay}(\mathbb {Z} _n,\mathbb {U} _n) $, the unitary Cayley Graphs of order $ n $, between
any pair of its vertices. With this result, we give the number of representations of a fixed
residue class $\bmod {} n $ as the sum of $ k $ units of $\mathbb {Z} _n $.
In this paper, we determine an explicit formula for the number of walks in , the unitary Cayley Graphs of order , between any pair of its vertices. With this result, we give the number of representations of a fixed residue class as the sum of units of .
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