Results 31 to 40 of about 22,931 (240)
On the degree of the Birkhoff polytope graph [PDF]
Mathematics and Computational SciencesThe Birkhoff polytope graph can be considered as the Cayley graph of the symmetric group $S_n$ with respect to $\mathcal{C}_n$, the set of cycles in $S_n$.
Bahman Khosravi, Behnam Khosravi
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Cayley graphs of basic algebraic structures [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We present simple graph-theoretic characterizations for the Cayley graphs of monoids, right-cancellative monoids, left-cancellative monoids, and groups.
Didier Caucal
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Finite BCI-groups are solvable [PDF]
International Journal of Group Theory, 2016 Let $S$ be a subset of a finite group $G$. The bi-Cayley graph ${rm BCay}(G,S)$ of $G$ with respect to $S$ is an undirected graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid xin G, sin S}$. A bi-Cayley graph ${rm BCay}(G,S)$ is
Majid Arezoomand, Bijan Taeri
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On the distance eigenvalues of Cayley graphs
پژوهشهای ریاضی, 2022 In this paper, graphs are undirected and loop-free and groups are finite. By Cn, Kn and Km,n we mean the cycle graph with n vertices, the complete graph with n vertices and the complete bipartite graph with parts size m and n, respectively.
Majid Arezoomand
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Parameters of the coprime graph of a group [PDF]
International Journal of Group Theory, 2021 There are many different graphs one can associate to a group. Some examples are the well-known Cayley graph, the zero divisor graph (of a ring), the power graph, and the recently introduced coprime graph of a group.
Jessie Hamm, Alan Way
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Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian [PDF]
, 2015 This note shows there are infinitely many finite groups G, such that every connected Cayley graph on G has a hamiltonian cycle, and G is not solvable. Specifically, for every prime p that is congruent to 1, modulo 30, we show there is a hamiltonian cycle
Morris, Dave Witte
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Quasirandom Cayley graphs [PDF]
Discrete Analysis, 2017 We prove that the properties of having small discrepancy and having small second eigenvalue are equivalent in Cayley graphs, extending a result of Kohayakawa, R dl, and Schacht, who treated the abelian case. The proof relies on Grothendieck's inequality. As a corollary, we also prove that a similar result holds in all vertex-transitive graphs.
Conlon, David, Zhao, Yufei
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Quartic integral Cayley graphs
Ars Mathematica Contemporanea, 2015 We give exhaustive lists of connected 4-regular integral Cayley graphs and connected 4-regular integral arc-transitive graphs. An integral graph is a graph for which all eigenvalues are integers. A Cayley graph Cay(Γ, S) for a given group Γ and connection set S ⊂ Γ is the graph with vertex set Γ and with a connected to b if and only if ba−1 ∈ S.
Minchenko, Marsha, Wanless, Ian M.
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Uniquely colorable Cayley graphs
Ars Mathematica Contemporanea, 2016 It is shown that the chromatic number χ ( G ) = k of a uniquely colorable Cayley graph G over a group Γ is a divisor of ∣Γ ∣ = n . Each color class in a k -coloring of G is a coset of a subgroup of order n / k of Γ . Moreover, it is proved that ( k − 1) n is a sharp lower bound for the number of edges of a uniquely k
Klotz, Walter, Sander, Torsten
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Color Energy Of A Unitary Cayley Graph
Discussiones Mathematicae Graph Theory, 2014 Let G be a vertex colored graph. The minimum number χ(G) of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al.
Adiga Chandrashekar +2 more
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