Power graphs and semigroups of matrices

By Andrei V. Kelarev, Stephen Quinn, R. Smolíková. Bulletin of the Australian Mathematical Society, 2001

90 citations recorded by the source corpus.

Matrices provide essential tools in many branches of mathematics, and matrix semigroups have applications in various areas. In this paper we give a complete description of all infinite matrix semigroups satisfying a certain combinatorial property defined in terms of power graphs.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/bf622034566328dc75b876f650ce05e4c760b6f4

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In Computational Theory and Mathematics

1. Andrei V. Kelarev
2. Ali Reza Ashrafi
3. Zeinab Mehranian
4. Ahmad Gholami

Citations in the corpus

• A combinatorial property and power graphs of semigroups (2004, background): “It is closely related to conditions considered earlier and leads to nontrivial interaction between graph, group and semigroup methods.”
• The Spectra of power graphs of certain finite groups (2017, background): “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.”
• Certain properties of the power graph associated with a finite group (2013, result): “For earlier results concerning these graphs we refer to [5, 6, 8, 20, 21, 22].”
• A note on the power graph of a finite group (2016, background): “These graphs were introduced in [6], see also [10, 11, 12].”
• A combinatorial property and Cayley graphs of semigroups (2002, background): “This question was answered in [12] and [13] for the cases of commutative and linear semigroups, respectively.”