A Study on Cayley Graphs of Full Transformation Semigroups

Riyas, A.; Anusha, P. U.; Geetha, K.

doi:10.1007/978-981-33-4842-4_2

Cited by 2 publications

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“…Investigations regarding Cayley graphs study graph properties such as connectedness, amenability, perfect matchings, algebraic degrees, chromatic and clique numbers or the existence of Hamiltonian paths [7][8][9][10]. The spectrum of the adjacency matrix of a Cayley graph allows interactions between graph, group representation and graph energy theories [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Brauer Analysis of Some Cayley and Nilpotent Graphs and Its Application in Quantum Entanglement Theory

Cañadas,

Gutierrez,

Mendez

2024

Symmetry

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Cayley and nilpotent graphs arise from the interaction between graph theory and algebra and are used to visualize the structures of some algebraic objects as groups and commutative rings. On the other hand, Green and Schroll introduced Brauer graph algebras and Brauer configuration algebras to investigate the algebras of tame and wild representation types. An appropriated system of multisets (called a Brauer configuration) induces these algebras via a suitable bounded quiver (or bounded directed graph), and the combinatorial properties of such multisets describe corresponding indecomposable projective modules, the dimensions of the algebras and their centers. Undirected graphs are examples of Brauer configuration messages, and the description of the related data for their induced Brauer configuration algebras is said to be the Brauer analysis of the graph. This paper gives closed formulas for the dimensions of Brauer configuration algebras (and their centers) induced by Cayley and nilpotent graphs defined by some finite groups and finite commutative rings. These procedures allow us to give examples of Hamiltonian digraph constructions based on Cayley graphs. As an application, some quantum entangled states (e.g., Greenberger–Horne–Zeilinger and Dicke states) are described and analyzed as suitable Brauer messages.

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Section: Introductionmentioning

confidence: 99%

“…Riyas and Geetha [8] presented a study on the Cayley graphs over dihedral groups. They gave conditions for subgraphs of Cayley graphs associated with dihedral groups to be bipartite or Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Brauer Analysis of Some Cayley and Nilpotent Graphs and Its Application in Quantum Entanglement Theory

Cañadas,

Gutierrez,

Mendez

2024

Symmetry

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show abstract

“…This would be a general result why the transformation semigroup is interesting to study. Several authors studied structural properties of Cayley graphs of transformation semigroups, see, for example [6] , [7] , [8] , [9] , [10] , [11] .…”

Section: Introductionmentioning

confidence: 99%

Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes

Nupo

Chaiya

2023

Heliyon

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A Study on Cayley Graphs of Full Transformation Semigroups

Cited by 2 publications

References 1 publication

Brauer Analysis of Some Cayley and Nilpotent Graphs and Its Application in Quantum Entanglement Theory

Brauer Analysis of Some Cayley and Nilpotent Graphs and Its Application in Quantum Entanglement Theory

Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes

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