Undirected power graphs of semigroups

By Ivy Chakrabarty, Shamik Ghosh, M. Sen. 2009

329 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/795e14830d0fae639f497bd8c3eb1710b4611bc9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Sriparna Chattopadhyay
2. Ali Reza Ashrafi
3. Zeinab Mehranian
4. Pratima Panigrahi
5. Ahmad Gholami

In Discrete Mathematics and Combinatorics

1. Ali Reza Ashrafi
2. Zeinab Mehranian
3. Wujie Shi
4. Huaquan Wei
5. Ahmad Gholami
6. A. Moghaddamfar
7. A. Skiba
8. Yanming Wang

In Geometry and Topology

1. Sriparna Chattopadhyay
2. Ali Reza Ashrafi
3. Zeinab Mehranian
4. Pratima Panigrahi
5. Ahmad Gholami
6. Angsuman Das
7. Yanming Wang
8. A. Skiba

Citations in the corpus

• The power graph of a finite group, II (2010, unknown): “These graphs have been defined and studied in [3], [4] (in the more general context of finite semigroups).”
• The coprime graph of a group (2014, background): “For more graphs, see [2, 3, 4, 7] Let G be a finite group.”
• The Spectra of power graphs of certain finite groups (2017, background): “The undirected power graph was introduced in [6], where it was shown that for a finite group G, P(G) is complete if and only if G is a cyclic group of order 1 or pm, for some prime number p and positive integer m.”
• Nonzero Component Graph of a Finite Dimensional Vector Space (2015, background): “ssue of colouring, this initiated the formal study of exposing the relationship between algebra and graph theory and at advancing applications of one to the other. Till then, a lot of research, e.g., [11, 2, 3, 1, 8, 6, 7, 4] has been done in connecting graph structures to various algebraic objects.”
• A note on the power graph of a finite group (2016, methodology): “In [4], it is proved that for a finite group G, P(G) is complete if and only if G is a cyclic group of order 1 or pm, for some prime number p and positive integer m.”
• Certain properties of the power graph associated with a finite group (2013, background): “For earlier results concerning these graphs we refer to [5, 6, 8, 20, 21, 22].”
• On Laplacian spectrum of power graphs of finite cyclic and dihedral groups (2015, background): “Then by [2] G(Zn) is the complete graph Kn and so G(Zn) is the null graph containing n isolated vertices.”