On the Independence Number of Cayley Digraphs of Rectangular Groups
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DOI: 10.1007/s00373-018-1896-6
Abstract: A rectangular group is isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. Some special cases of rectangular groups consisting of left groups and right groups are… read more here.
Keywords: mathrm cay; rectangular groups; cayley; cay cay ... See more keywords
On groups all of whose Haar graphs are Cayley graphs
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DOI: 10.1007/s10801-019-00894-7
Abstract: A Cayley graph of a group H is a finite simple graph $$\Gamma $$ Γ such that $$\mathrm{Aut}(\Gamma )$$ Aut ( Γ ) contains a subgroup isomorphic to H acting regularly on $$V(\Gamma ),$$ V… read more here.
Keywords: graphs; cayley; whose haar; graph ... See more keywords
On the second largest eigenvalue of some Cayley graphs of the symmetric group
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DOI: 10.1007/s10801-021-01080-4
Abstract: Let $$S_n$$ S n and $$A_{n}$$ A n denote the symmetric and alternating group on the set $$\{1,\ldots ,n\},$$ { 1 , … , n } , respectively. In this paper we are interested in… read more here.
Keywords: gamma; lambda gamma; cayley; second largest ... See more keywords
Spherical Model on a Cayley Tree: Large Deviations
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DOI: 10.1007/s10955-016-1696-4
Abstract: We study the spherical model of a ferromagnet on a Cayley tree and show that in the case of empty boundary conditions a ferromagnetic phase transition takes place at the critical temperature $$T_\mathrm{c} =\frac{6\sqrt{2}}{5}J$$Tc=625J, where… read more here.
Keywords: temperature; cayley; spherical model; frac ... See more keywords
The Cayley Grassmannian
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DOI: 10.1016/j.jalgebra.2018.02.010
Abstract: We study the projective variety CG parametrizing four dimensional subalgebras of the complex octonions, which we call the Cayley Grass-mannian. We prove that it is a spherical G2-variety with only three orbits that we describe… read more here.
Keywords: cayley; cayley grassmannian;
Elevated effective dimension in tree-like nanomagnetic Cayley structures.
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DOI: 10.1039/c9nr07510k
Abstract: Using state-of-the-art electron-beam lithography, Ising-type nanomagnets may be defined onto nearly any two-dimensional pattern imaginable. The ability to directly observe magnetic configurations achieved in such artificial spin systems makes them a perfect playground for the… read more here.
Keywords: effective dimension; cayley; tree; artificial spin ... See more keywords
State transfer on two-fold Cayley trees via quantum walks
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DOI: 10.1088/1674-1056/abcfa1
Abstract: Perfect state transfer (PST) has great significance due to its applications in quantum information processing and quantum computation. The main problem we study in this paper is to determine whether the two-fold Cayley tree, an… read more here.
Keywords: quantum walk; quantum; state transfer; cayley ... See more keywords
The Energy of Cayley Graphs for a Generating Subset of the Dihedral Groups
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DOI: 10.11113/matematika.v35.n3.1115
Abstract: Let G be a finite group and S be a subset of G where S does not include the identity of G and is inverse closed. A Cayley graph of a group G with respect… read more here.
Keywords: energy cayley; energy; cayley; cayley graphs ... See more keywords
On tetravalent s-regular Cayley graphs
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DOI: 10.1142/s021949881750195x
Abstract: A Cayley graph Γ = Cay(G,S) is said to be core-free if G is core-free in some X for G ≤ X ≤AutΓ. A graph Γ is called s-regular if AutΓ acts regularly on its… read more here.
Keywords: cayley; tetravalent regular; cayley graphs; regular cayley ... See more keywords
Certain Structural Properties for the Direct Product of Cayley Graphs and Their Theoretical Applications
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DOI: 10.1155/2024/8825307
Abstract: Symmetry properties are of vital importance for graphs. The famous Cayley graph is a good mathematical model as its high symmetry. The normality of the graph can well reflect the symmetry of the graph. In… read more here.
Keywords: cayley graphs; direct product; cayley; product cayley ... See more keywords
Extremality of Disordered Phase of λ-Model on Cayley Trees
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DOI: 10.3390/a15010018
Abstract: In this paper, we consider the λ-model for an arbitrary-order Cayley tree that has a disordered phase. Such a phase corresponds to a splitting Gibbs measure with free boundary conditions. In communication theory, such a… read more here.
Keywords: cayley; extremality disordered; disordered phase; phase model ... See more keywords