Walks on Unitary Cayley Graphs and Applications

Details Walks on Unitary Cayley Graphs and Applications Walks on Unitary Cayley Graphs and Applications

2012-03-12

arxiv.org/abs/1203.2473v1

Mathematics

Combinatorics

Scientific paper

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 $\mathbb{Z}_n$.

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