Irregular Labellings of Circulant Graphs

2011/11/01 by Marcin Anholcer, Anholcer, Marcin
Computer Science · Engineering · Mathematics · #05C78 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1111.0316

openalex publication_date 2011/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the irregularity strength (s(G)) and total vertex irregularity strength (tvs(G)) of circulant graphs Ci_n(1,2,...,k) and prove that tvs(Ci_n(1,2,...,k))=\lceil(n+2k)/(2k+1)\rceil, while s(Ci_n(1,2,...,k))=\lceil(n+2k-1)/(2k)\rceil except the case when (n \bmod 4k = 2k+1 \wedge k\bmod 2=1) \vee n=2k+1 and s(Ci_n(1,2,...,k))=\lceil(n+2k-1)/(2k)\rceil+1.

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