The endomorphism monoids and automorphism groups of Cayley graphs of semigroups
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DOI: 10.1007/s00233-017-9875-4
Abstract: In this note, we introduce the notions of color-permutable automorphisms and color-permutable vertex-transitive Cayley graphs of semigroups. As a main result, for a finite monoid S and a generating set C of S, we explicitly… read more here.
Keywords: graphs semigroups; color; endomorphism; automorphism ... See more keywords
The second largest eigenvalues of some Cayley graphs on alternating groups
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DOI: 10.1007/s10801-018-0843-1
Abstract: Let $$A_n$$An denote the alternating group of degree n with $$n\ge 3$$n≥3. The alternating group graph $$AG_n$$AGn, extended alternating group graph $$EAG_n$$EAGn and complete alternating group graph $$CAG_n$$CAGn are the Cayley graphs $$\mathrm {Cay}(A_n,T_1)$$Cay(An,T1), $$\mathrm… read more here.
Keywords: second largest; alternating group; cayley graphs; largest eigenvalues ... See more keywords
Testing Isomorphism of Central Cayley Graphs Over Almost Simple Groups in Polynomial Time
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DOI: 10.1007/s10958-018-3998-3
Abstract: A Cayley graph over a group G is said to be central if its connection set is a normal subset of G. It is proved that for any two central Cayley graphs over explicitly given… read more here.
Keywords: simple groups; almost simple; time; cayley graphs ... See more keywords
On transitivity and connectedness of Cayley graphs of gyrogroups
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DOI: 10.1016/j.heliyon.2021.e07049
Abstract: In this work, we explore edge direction, transitivity, and connectedness of Cayley graphs of gyrogroups. More specifically, we find conditions for a Cayley graph of a gyrogroup to be undirected, transitive, and connected. We also… read more here.
Keywords: transitivity connectedness; graphs gyrogroups; cayley graphs; connectedness cayley ... See more keywords
On the signed domination number of some Cayley graphs
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DOI: 10.1080/00927872.2020.1722830
Abstract: Abstract A signed dominating function of graph Γ is a function such that for each The signed domination number is the minimum weight of a signed dominating function on Γ. Let be a finite group… read more here.
Keywords: number cayley; domination number; signed domination; cayley graphs ... See more keywords
Dual-CISTs: Configuring a Protection Routing on Some Cayley Networks
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DOI: 10.1109/tnet.2019.2910019
Abstract: A set of $k~(\geqslant 2)$ spanning trees in the underlying graph of a network topology is called completely independent spanning trees, (CISTs for short), if they are pairwise edge-disjoint and inner-node-disjoint. Particularly, if $k=2$ ,… read more here.
Keywords: protection; dual cists; cayley graphs; dual cist ... 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
Cayley Graphs over LA-Groups and LA-Polygroups
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DOI: 10.1155/2021/4226232
Abstract: The purpose of this paper is the study of simple graphs that are generalized Cayley graphs over LA-polygroups . In this regard, we construct two new extensions for building LA-polygroups. Then, we define Cayley graph… read more here.
Keywords: gclap graph; graphs groups; groups polygroups; graph ... See more keywords
Some Resolving Parameters in a Class of Cayley Graphs
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DOI: 10.1155/2022/9444579
Abstract: Resolving parameters are a fundamental area of combinatorics with applications not only to many branches of combinatorics but also to other sciences. In this study, we construct a class of Toeplitz graphs and will be… read more here.
Keywords: cayley graphs; class; class graphs; resolving parameters ... See more keywords
Directed Strongly Regular Cayley Graphs over Metacyclic Groups of Order 4n
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DOI: 10.3390/math7111011
Abstract: We construct several new families of directed strongly regular Cayley graphs (DSRCGs) over the metacyclic group M 4 n = ⟨ a , b | a n = b 4 = 1 , b −… read more here.
Keywords: directed strongly; strongly regular; regular cayley; cayley graphs ... See more keywords