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On transitivity and connectedness of Cayley graphs of gyrogroups [PDF]
Heliyon, 2021 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.
Rasimate Maungchang +3 more
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Hamiltonian Normal Cayley Graphs
Discussiones Mathematicae Graph Theory, 2019 A variant of the Lovász Conjecture on hamiltonian paths states that every finite connected Cayley graph contains a hamiltonian cycle. Given a finite group G and a connection set S, the Cayley graph Cay(G, S) will be called normal if for every g ∈ G we ...
Montellano-Ballesteros Juan José +1 more
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Edge-Transitivity of Cayley Graphs Generated by Transpositions
Discussiones Mathematicae Graph Theory, 2016 Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note,
Ganesan Ashwin
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Integral Cayley graphs and groups [PDF]
SIAM Journal on Discrete Mathematics, 2013 We solve two open problems regarding the classification of certain classes of Cayley graphs with integer eigenvalues. We first classify all finite groups that have a "non-trivial" Cayley graph with integer eigenvalues, thus solving a problem proposed by ...
Ahmady, Azhvan +2 more
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Algebra and Logic, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, W. +3 more
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Cayley and Tutte polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Cayley polytopes were defined recently as convex hulls of Cayley compositions introduced by Cayley in 1857. In this paper we resolve Braun's conjecture, which expresses the volume of Cayley polytopes in terms of the number of connected graphs.
Matjaž Konvalinka, Igor Pak
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The Electronic Journal of Combinatorics, 2022 We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.
Liu, Xiaogang, Zhou, Sanming
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Domination in Cayley graphs: A survey
AKCE International Journal of Graphs and Combinatorics, 2019 Let Ω be a symmetric generating set of a finite group Γ. Assume that (Γ,Ω)be such that Γ=〈Ω〉and Ω satisfies the two conditions C1: the identity element e∉Ω and C2: if a∈Ω, then a−1∈Ω. Given (Γ,Ω)satisfying C1and C2, define a Cayley graph G=Cay(Γ,Ω)with V(
T. Tamizh Chelvam, M. Sivagami
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Approximating Cayley Diagrams Versus Cayley Graphs [PDF]
Combinatorics, Probability and Computing, 2012 We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that converge to the same limit, and such that a Hamiltonian cycle in one of them has a limit that is not approximable by ...
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Cayley Bipolar Fuzzy Graphs [PDF]
The Scientific World Journal, 2013 We introduce the concept of Cayley bipolar fuzzy graphs and investigate some of their properties. We present some interesting properties of bipolar fuzzy graphs in terms of algebraic structures. We also discuss connectedness in Cayley bipolar fuzzy graphs.
N. O. Alshehri, Muhammad Akram
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