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Generalized Cayley graphs

1992
*
Discrete Mathematics
*

Zf B(X) is connected, then B(X) is a

doi:10.1016/0012-365x(92)90121-u
fatcat:ic7xdg4qrra23jdmzkf23pmkye
*Cayley**graph*if and only if X is a*generalized**Cayley**graph*, Proof. ... We shall now introduce the concept of*generalized**Cayley**graphs*. ...##
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Isomorphisms of generalized Cayley graphs

2018
*
Ars Mathematica Contemporanea
*

In this paper, we investigate the isomorphism problems of the

doi:10.26493/1855-3974.1345.ae6
fatcat:dajpugqm45cqtlt4imyylm4rxq
*generalized**Cayley**graphs*, which are*generalizations*of the traditional*Cayley**graphs*. ... We find that there are two types of natural isomorphisms for the*generalized**Cayley**graphs*. ... Thus GC(G, {1}, α) is a*generalized**Cayley**graph*of G. Also, GC(G, {2}, 1) is a*generalized**Cayley**graph*of G. ...##
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Cellular automata over generalized Cayley graphs

2017
*
Mathematical Structures in Computer Science
*

We propose a notion of

doi:10.1017/s0960129517000044
fatcat:rrsg6zukbverfjnxyqan2ekbdu
*graphs*, which preserves or*generalizes*these features. Whereas*Cayley**graphs*are very regular,*generalized**Cayley**graphs*are arbitrary, although of a bounded degree. ...*Cayley**graphs*have a number of useful features: the ability to graphically represent finitely*generated*group elements and their relations; to name all vertices relative to an origin; and the fact that ...*Graphs*as languages*Generalized**Cayley**graphs*. ...##
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Graph product of generalized Cayley graphs over polygroups

2019
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Algebraic structures and their applications
*

In this paper, we introduce a suitable

doi:10.29252/asta.6.1.49
fatcat:24xcpktffjeqjnhkfrkbmdfi5u
*generalization*of*Cayley**graphs*that is defined over polygroups (GCP-*graph*) and give some examples and properties. ... Then, we mention a*generalization*of NEPS that contains some known*graph*operations and apply to GCP-*graphs*. Finally, we prove that the product of GCP-*graphs*is again a GCP-*graph*. ... Then we define the*generalized**Cayley**graph*GCP(P; S) as a simple*graph*with vertex set P and edge set Example 2. 2 . 2 The*generalized**Cayley**graph*of the polygroup P 2 = ⟨{1, 2, 3, 4}, •, 1, −1 ⟩ and ...##
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Asymptotic pressure on Cayley graphs of finitely generated semigroups
[article]

2021
*
arXiv
*
pre-print

The vertices of the

arXiv:2106.16246v4
fatcat:rzv4sp5xj5fa7pxegusdgwac34
*Cayley**graph*of a finitely*generated*semigroup form a set of sites which can be labeled by elements of a finite alphabet in a manner governed by a nonnegative real interaction matrix ... We prove that for shifts of finite type on*generalized*Fibonacci trees, under an added condition, the limit exists and is given by an infinite series. ... (If r = 0, so that R ij = 1 for all i, j, S is the free semigroup on k*generators*and its*Cayley**graph*is the full k-tree.) ...##
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Cayley graphs of finitely generated groups

2005
*
Proceedings of the American Mathematical Society
*

There does not exist a Borel choice of

doi:10.1090/s0002-9939-05-07987-6
fatcat:ulqefovl3bgrjcz3ozyltfai3e
*generators*for each finitely*generated*group which has the property that isomorphic groups are assigned isomorphic*Cayley**graphs*. ... Of course, if G is an arbitrary finitely*generated*group, then G does not have a "canonical" finite*generating*set S; and if S, S ⊆ G 1 are different finite*generating*sets, then the*Cayley**graphs*Cay( ... Our proof is based upon the observation that the classification problem for finitely*generated*groups is much more difficult than that for*Cayley**graphs*. ...##
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CAYLEY GRAPHS OF GENERALIZED DIHEDRAL GROUPS
[chapter]

1981
*
Zero-Symmetric Graphs
*

Also the Estrada index of Γ, which is defined in 2000 by Ernesto Estrada, is defined as In this paper, we compute the eigenvalues, energy and Estrada index of

doi:10.1016/b978-0-12-194580-0.50028-8
fatcat:vzpwb2sjyndzxk4g3jegv52uj4
*Cayley**graphs*on*generalized*dihedral groups ... As an application, we compute these items for honeycomb toroidal*graphs*and*Cayley**graphs*on dihedral groups. ... Semi-*Cayley**graphs*which are a*generalization*of*Cayley**graphs*defined by Resmini and Jungnickel [12] , see also [3] . ...##
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Construction of Directed Strongly Regular Graphs as Generalized Cayley Graphs
[article]

2014
*
arXiv
*
pre-print

In this paper, an infinite family of directed strongly regular

arXiv:1410.1161v2
fatcat:jesqb5fb2zfo7lf7mwzcpigrqu
*graphs*is constructed, as*generalized**Cayley**graphs*of cyclic groups. ... Directed strongly regular*graphs*were introduced by Duval in 1998 as one of the possible*generalization*of classical strongly regular*graphs*to the directed case. ... In section 2, we give the definition of*generalized**Cayley**graphs*and a necessary and sufficient condition that makes it easy to check whether a*generalized**Cayley**graph*is a DSRG. ...##
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Automorphisms of Cayley graphs generated by transposition sets
[article]

2013
*
arXiv
*
pre-print

It is shown that the automorphism group of the

arXiv:1303.5974v2
fatcat:v4fxosaknjctbby3zam4w7dkbq
*Cayley**graph*of the permutation group H*generated*by S is the semidirect product R(H) (H,S), where R(H) is the right regular representation of H and (H,S) ... This result is a common*generalization*of previous results by Feng, Ganesan, Harary, Mirafzal, and Zhang and Huang. ... Thus, this*Cayley**graph*Cay(S 4 , S) is not normal. In all of the papers mentioned above on*Cayley**graphs**generated*by transpositions, the set of transpositions S is assumed to*generate*S n . ...##
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Which finitely generated Abelian groups admit isomorphic Cayley graphs?

2012
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Geometriae Dedicata
*

We show that

doi:10.1007/s10711-012-9761-x
fatcat:phelagp3brfaxkipvoakrnlyk4
*Cayley**graphs*of finitely*generated*Abelian groups are rather rigid. ... As a consequence we obtain that two finitely*generated*Abelian groups admit isomorphic*Cayley**graphs*if and only if they have the same rank and their torsion parts have the same cardinality. ...*Cayley**graphs*. ...##
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A note on vertex-transitive non-Cayley graphs from Cayley graphs generated by involutions

2010
*
Discrete Mathematics
*

*graphs*from

*Cayley*

*graphs*

*generated*by involutions. ... We show that the result of Watkins (1990) [19] on constructing vertex-transitive non-

*Cayley*

*graphs*from line

*graphs*yields a simple method that produces infinite families of vertex-transitive non-

*Cayley*... Indirect methods try to identify structural properties of

*Cayley*

*graphs*which they do not share with vertex-transitive

*graphs*in

*general*. ...

##
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Automorphism groups of Cayley graphs generated by connected transposition sets

2013
*
Discrete Mathematics
*

Let S be a set of transpositions that

doi:10.1016/j.disc.2013.07.013
fatcat:rkmrl5rsrvenpgfzb2npd5khte
*generates*the symmetric group S_n, where n > 3. The transposition*graph*T(S) is defined to be the*graph*with vertex set {1,... ... We thus identify the existence of 4-cycles in the transposition*graph*as being an important factor in causing a potentially larger automorphism group of the*Cayley**graph*. ... A special case of this Corollary whereby T (S) is a tree gives the result of Feng [3] that the automorphism group of a*Cayley**graph**generated*by a transposition tree is isomorphic to R(S n ) ⋊ Aut(S ...##
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Neighbourhood Graphs of Cayley Graphs for Finitely-generated Groups

2002
*
European journal of combinatorics (Print)
*

In this short note the neighbourhood

doi:10.1006/eujc.2002.0596
fatcat:r4ojenmhnjhj5fsr37tfht26vi
*graph*of a*Cayley**graph*is considered. It has as nodes a symmetric*generating*set of a finitely-*generated*group Γ. ... Two nodes are connected by an edge if one is obtained from the other by multiplication on the right by one of the*generators*. Two necessary conditions on the*graphs*are shown. ... Let now S be a finite symmetric*generating*set of a finitely-*generated*group Γ. The neighbourhood*graph*(S, K) of 1 ∈ Γ of the*Cayley**graph*of Γ with respect to S with edges K will be investigated. ...##
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Diameter of Cayley graphs of permutation groups generated by transposition trees
[article]

2011
*
arXiv
*
pre-print

Let Γ be a

arXiv:1111.3114v3
fatcat:7bbu7j7cw5enbkgrewyc464cly
*Cayley**graph*of the permutation group*generated*by a transposition tree T on n vertices. ... In an oft-cited paper Akers:Krishnamurthy:1989 (see also Hahn:Sabidussi:1997), it is shown that the diameter of the*Cayley**graph*Γ is bounded as (Γ) <_π∈ S_nc(π)-n+∑_i=1^n _T(i,π(i)), where the maximization ... Let Γ be the*Cayley**graph**generated*by transposition tree T . ...##
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On a diameter bound for Cayley graphs generated by transposition trees
[article]

2011
*
arXiv
*
pre-print

Let Γ be a

arXiv:1106.5353v3
fatcat:mjvvuqnr5vbexn5kvi2ayn26pe
*Cayley**graph**generated*by a transposition tree. A natural problem is to understand how the properties of the*Cayley**graph*depend on those of the underlying transposition tree. ... However, it can be verified that the diameter of the*Cayley**graph**generated*by T is 14. ... Thus, when we study the sharpness (or lack thereof) of the upper bounds, we assume throughout that T is a tree and Γ is the*Cayley**graph**generated*by a tree. ...
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