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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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Perfect Codes in Cayley Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2018 This is the final version that will appear in SIAM J.
Binzhou Xia, Sanming Zhou
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Neighborhood degree sum-based molecular descriptors of fractal and Cayley tree dendrimers [PDF]
European Physical Journal Plus, 2021 Sourav Mondal, Nilanjan De, Anita Pal
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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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