Notes on the Co-prime Order Graph of a Group
Keywords:co-prime order graph, vertex-connectivity, group
The co-prime order graph of a group $$G$$ is the graph with vertex set $$G$$, and two distinct elements $$x,y\in G$$ are adjacent if gcd$$(o(x),o(y))$$ is either $$1$$ or a prime, where $$o(x)$$ and $$o(y)$$ are the orders of $$x$$ and $$y$$, respectively. In this paper, we characterize finite groups whose co-prime order graphs are complete and classify finite groups whose co-prime order graphs are
planar, which generalizes some results by Banerjee . We also compute the vertex-connectivity of the co-prime order graph of a cyclic group, a dihedral group and a generalized quaternion group, which answers a question by Banerjee .
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LicenseCopyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences
Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences
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