Refereed journal article or data article (A1)

Optimal bounds on codes for location in circulant graphs




List of AuthorsVille Junnila, Tero Laihonen, Gabrielle Paris

PublisherSPRINGER

Publication year2019

JournalCryptography and Communications

Journal acronymCRYPTOGR COMMUN

Volume number11

Issue number4

Start page621

End page640

Number of pages20

ISSN1936-2447

eISSN1936-2455

DOIhttp://dx.doi.org/10.1007/s12095-018-0316-3

Self-archived copy’s web addresshttps://research.utu.fi/converis/portal/detail/Publication/41355929


Abstract
Identifying and locating-dominating codes have been studied widely in circulant graphs of type Cn(1,2,3,...,r) over the recent years. In 2013, Ghebleh and Niepel studied locating-dominating and identifying codes in the circulant graphs Cn(1,d) for d=3 and proposed as an open question the case of d>3. In this paper we study identifying, locating-dominating and self-identifying codes in the graphs Cn(1,d), Cn(1,d-1,d) and Cn(1,d-1,d,d+1). We give a new method to study lower bounds for these three codes in the circulant graphs using suitable grids. Moreover, we show that these bounds are attained for infinitely many parameters n and d. In addition, new approaches are provided which give the exact values for the optimal self-identifying codes in Cn(1,3) and Cn(1,4).

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Last updated on 2022-07-04 at 17:25