Abstract
In this sequel paper, we continue our study on co-maximal subgroup graph \(\Gamma (G)\) of a group G. We discuss some further results on connectedness and when \(\Gamma (G)\) is edgeless. Moreover, we study the independence number, chromatic number and perfectness of \(\Gamma (G)\). In the process, we show that if the independence number is suitably small, then the underlying group is solvable. We also classify co-maximal subgroup graphs of certain groups upto isomorphism.
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Acknowledgements
The authors acknowledge the funding of DST-FIST Sanction no. \(SR/FST/MS-I/2019/41\) and DST-SERB-MATRICS Sanction no. MTR/2022/000020, Govt. of India. The authors are also grateful to Professor Peter Cameron for fruitful discussions regarding the connectedness of comaximal subgroup graphs.
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Das, A., Saha, M. On co-maximal subgroup graph of a group-II. Ricerche mat (2023). https://doi.org/10.1007/s11587-023-00836-3
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DOI: https://doi.org/10.1007/s11587-023-00836-3