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Efficient k-Distance Dominating Set in Cayley Graphs

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Abstract

The efficient k-distance domination number \(\gamma ^{k}_{e}(G)\) is the minimum among the cardinalities of efficient k-distance dominating sets of G. Upper bound in terms of order and maximum degree of an independent set S of vertices in a graph \(G=(V,E)\) called an efficient k-distance dominating set if every vertex in \(V-S\) be distance k from exactly one vertex in S has been presented. Sufficient conditions for 3-regular Cayley graphs to have disjoint efficient k-distance dominating sets are given. Characterization of the 3-regular connected circulant graphs that admit an efficient k-distance dominating set for \(k=2,3\) has been obtained.

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Authors and Affiliations

  1. Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, Post Code:47148-71167, Iran

    H. Abdollahzadeh Ahangar

  2. Department of Mathematics, University of Mazandaran, Babolsar, Iran

    D. A. Mojdeh

  3. Department of Mathematics, University of Tafresh, Tafresh, Iran

    A. Sayed-Khalkhali

  4. Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, Hristo Smirnenski 1 Blv., 1046, Sofia, Bulgaria

    V. Samodivkin

Authors
  1. H. Abdollahzadeh Ahangar
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  2. D. A. Mojdeh
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  3. A. Sayed-Khalkhali
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  4. V. Samodivkin
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Correspondence to H. Abdollahzadeh Ahangar.

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Abdollahzadeh Ahangar, H., Mojdeh, D.A., Sayed-Khalkhali, A. et al. Efficient k-Distance Dominating Set in Cayley Graphs. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90, 141–147 (2020). https://doi.org/10.1007/s40010-018-0539-x

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  • DOI: https://doi.org/10.1007/s40010-018-0539-x

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