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Generalized Cayley graphs
1992
Discrete Mathematics
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Zf B(X) is connected, then B(X) is a Cayley graph if and only if X is a generalized Cayley graph, Proof. ...
We shall now introduce the concept of generalized Cayley graphs. ...
doi:10.1016/0012-365x(92)90121-u
fatcat:ic7xdg4qrra23jdmzkf23pmkye
Isomorphisms of generalized Cayley graphs
2018
Ars Mathematica Contemporanea
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In this paper, we investigate the isomorphism problems of the 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. ...
doi:10.26493/1855-3974.1345.ae6
fatcat:dajpugqm45cqtlt4imyylm4rxq
Cellular automata over generalized Cayley graphs
2017
Mathematical Structures in Computer Science
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We propose a notion of 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. ...
doi:10.1017/s0960129517000044
fatcat:rrsg6zukbverfjnxyqan2ekbdu
Graph product of generalized Cayley graphs over polygroups
2019
Algebraic structures and their applications
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In this paper, we introduce a suitable 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 ...
doi:10.29252/asta.6.1.49
fatcat:24xcpktffjeqjnhkfrkbmdfi5u
Asymptotic pressure on Cayley graphs of finitely generated semigroups
[article]
2021
arXiv
pre-print
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The vertices of the 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.) ...
arXiv:2106.16246v4
fatcat:rzv4sp5xj5fa7pxegusdgwac34
Cayley graphs of finitely generated groups
2005
Proceedings of the American Mathematical Society
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There does not exist a Borel choice of 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. ...
doi:10.1090/s0002-9939-05-07987-6
fatcat:ulqefovl3bgrjcz3ozyltfai3e
CAYLEY GRAPHS OF GENERALIZED DIHEDRAL GROUPS
[chapter]
1981
Zero-Symmetric Graphs
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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 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] . ...
doi:10.1016/b978-0-12-194580-0.50028-8
fatcat:vzpwb2sjyndzxk4g3jegv52uj4
Construction of Directed Strongly Regular Graphs as Generalized Cayley Graphs
[article]
2014
arXiv
pre-print
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2014 pre-print arXiv:1410.1161v1 fatcat:pdjw7ngbg5frzd43n76bfwrapm
In this paper, an infinite family of directed strongly regular 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. ...
arXiv:1410.1161v2
fatcat:jesqb5fb2zfo7lf7mwzcpigrqu
Automorphisms of Cayley graphs generated by transposition sets
[article]
2013
arXiv
pre-print
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It is shown that the automorphism group of the 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 . ...
arXiv:1303.5974v2
fatcat:v4fxosaknjctbby3zam4w7dkbq
Which finitely generated Abelian groups admit isomorphic Cayley graphs?
2012
Geometriae Dedicata
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We show that 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. ...
doi:10.1007/s10711-012-9761-x
fatcat:phelagp3brfaxkipvoakrnlyk4
A note on vertex-transitive non-Cayley graphs from Cayley graphs generated by involutions
2010
Discrete Mathematics
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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. ...
doi:10.1016/j.disc.2009.07.022
fatcat:mdt5crix3ffy5hbtzigygzu7xu
Automorphism groups of Cayley graphs generated by connected transposition sets
2013
Discrete Mathematics
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2012 pre-print arXiv:1205.5199v3 fatcat:7nb4ptopgnfapcuu2g76ikzryqOther Versions
Let S be a set of transpositions that 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 ...
doi:10.1016/j.disc.2013.07.013
fatcat:rkmrl5rsrvenpgfzb2npd5khte
Neighbourhood Graphs of Cayley Graphs for Finitely-generated Groups
2002
European journal of combinatorics (Print)
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In this short note the neighbourhood 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. ...
doi:10.1006/eujc.2002.0596
fatcat:r4ojenmhnjhj5fsr37tfht26vi
Diameter of Cayley graphs of permutation groups generated by transposition trees
[article]
2011
arXiv
pre-print
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Let Γ be a 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 . ...
arXiv:1111.3114v3
fatcat:7bbu7j7cw5enbkgrewyc464cly
On a diameter bound for Cayley graphs generated by transposition trees
[article]
2011
arXiv
pre-print
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2011 pre-print arXiv:1106.5353v2 fatcat:litsx6wag5e4dbrg6ijjgktqleOther Versions
Let Γ be a 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. ...
arXiv:1106.5353v3
fatcat:mjvvuqnr5vbexn5kvi2ayn26pe
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