A Combinatorial Property and Power Graphs of Groups

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Power graphs and semigroups of matrices (2001, unknown): “[9] Let D = {V,E) be a graph with E / 0 and let H be an infinite group.”
A combinatorial property and Cayley graphs of semigroups (2002, methodology): “In [10] the authors described all groups G and graphs D such that G is power D-saturated.”
A combinatorial property and power graphs of semigroups (2004, methodology): “A new combinatorial property was introduced in [10] using power graphs.”
Graphs defined on groups (2021, methodology): “The power graph was introduced by Kelarev and Quinn [71].”
A note on the power graph of a finite group (2016, background): “These graphs were introduced in [6], see also [10, 11, 12].”
The Spectra of power graphs of certain finite groups (2017, methodology): “Kelarev, Quinn and Smolíková [4] gave a complete description of all infinite matrix semigroups satisfying a certain combinatorial property defined in terms of power graphs.”