Abstract
A rectangular group is isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. Some special cases of rectangular groups consisting of left groups and right groups are also considered here. Let \( \mathrm {Cay}(S,A) \) denote the Cayley digraph of the rectangular group S with the connection set A. In this paper, we are interested in studying some properties of \( \mathrm {Cay}(S,A) \) such as the independence, weakly independence, path independence, and weakly path independence. Furthermore, the independence numbers for those properties of \( \mathrm {Cay}(S,A) \) are also determined.
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Acknowledgements
The authors would like to thank the referees for their useful comments and valuable suggestions on the manuscript. This research was supported by Chiang Mai University.
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Panma, S., Nupo, N. On the Independence Number of Cayley Digraphs of Rectangular Groups. Graphs and Combinatorics 34, 579–598 (2018). https://doi.org/10.1007/s00373-018-1896-6
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DOI: https://doi.org/10.1007/s00373-018-1896-6