Results 31 to 40 of about 20,494 (188)
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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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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Mixed Moore Cayley Graphs [PDF]
Journal of Interconnection Networks, 2017 The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. There has been much recent interest in the problem for mixed graphs, where we allow both undirected edges and directed arcs in the graph.
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Labelled tree graphs, Feynman diagrams and disk integrals
Journal of High Energy Physics, 2017 In this note, we introduce and study a new class of “half integrands” in Cachazo-He-Yuan (CHY) formula, which naturally generalize the so-called Parke-Taylor factors; these are dubbed Cayley functions as each of them corresponds to a labelled tree graph.
Xiangrui Gao, Song He, Yong Zhang
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Constructing Independent Spanning Trees on Pancake Networks
IEEE Access, 2020 For any graph G, the set of independent spanning trees (ISTs) is defined as the set of spanning trees in G. All ISTs have the same root, paths from the root to another vertex between distinct trees are vertex-disjoint and edge-disjoint.
Dun-Wei Cheng +2 more
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