Irregular labelings of circulant graphs

Marcin Anholcer; Cory Palmer

doi:10.1016/j.disc.2012.06.017

Irregular labelings of circulant graphs

Marcin Anholcer, Cory Palmer

Mathematics

Poznan University of Economics and Business

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

Abstract

We investigate the irregularity strength (s(G)) and total vertex irregularity strength (tvs(G)) of circulant graphs Cⁱⁿ(1,2,⋯, k) and prove that tvs(Cⁱⁿ(1,2,⋯,k))=n+2k/2k+1⌉, while s(Cⁱⁿ(1,2,⋯,k))=n+2k-1/2k⌉ except if either n=2k+1 or if k is odd and n≡2k+1(mod4k), then s(Cⁱⁿ(1,2,⋯,k))=n+2k- 12k⌉+1.

Original language	English
Pages (from-to)	3461-3466
Number of pages	6
Journal	Discrete Mathematics
Volume	312
Issue number	23
DOIs	https://doi.org/10.1016/j.disc.2012.06.017
State	Published - Dec 6 2012

Keywords

Circulant graph
Graph labeling
Graph weighting
Irregularity strength
Total vertex irregularity strength

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10.1016/j.disc.2012.06.017

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abstract = "We investigate the irregularity strength (s(G)) and total vertex irregularity strength (tvs(G)) of circulant graphs Cin(1,2,⋯, k) and prove that tvs(Cin(1,2,⋯,k))=n+2k/2k+1⌉, while s(Cin(1,2,⋯,k))=n+2k-1/2k⌉ except if either n=2k+1 or if k is odd and n≡2k+1(mod4k), then s(Cin(1,2,⋯,k))=n+2k- 12k⌉+1.",

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author = "Marcin Anholcer and Cory Palmer",

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AB - We investigate the irregularity strength (s(G)) and total vertex irregularity strength (tvs(G)) of circulant graphs Cin(1,2,⋯, k) and prove that tvs(Cin(1,2,⋯,k))=n+2k/2k+1⌉, while s(Cin(1,2,⋯,k))=n+2k-1/2k⌉ except if either n=2k+1 or if k is odd and n≡2k+1(mod4k), then s(Cin(1,2,⋯,k))=n+2k- 12k⌉+1.

KW - Circulant graph

KW - Graph labeling

KW - Graph weighting

KW - Irregularity strength

KW - Total vertex irregularity strength

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SP - 3461

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JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Irregular labelings of circulant graphs

Abstract

Keywords

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