Walks on Unitary Cayley Graphs and Applications

2012/03/12 by Elias Cancela, Cancela, Elias, Daniel A. Jaume +6
Computer Science · Engineering · Mathematics · #05C25 #05C50 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT) #graph theory and CDMA systems #math.CO #math.NT #msc:05C25 #msc:05C50

paper · pdf · doi:10.48550/arxiv.1203.2473

arxiv created 2012/03/12 · openalex publication_date 2012/03/12 · arxiv updated 2012/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we determine an explicit formula for the number of walks in X_n = \textsfCay(ℤ_n,\mathbbU_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 \bmodn as the sum of k units of ℤ_n.

Citations

• On the addition of units and nonunits mod m

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