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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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