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Spectra of twists of Cayley and Cayley sum graphs

Advances in Applied Mathematics, 2022
Let $G$ be a finite group with $|G|\geq 4$ and $S$ be a subset of $G$. Given an automorphism $σ$ of $G$, the twisted Cayley graph $C(G, S)^σ$ (resp. the twisted Cayley sum graph $C_Σ(G, S)^σ$) is defined as the graph having $G$ as its set of vertices and the adjacent vertices of a vertex $g\in G$ are of the form $σ(gs)$ (resp.
Arindam Biswas 0003, Jyoti Prakash Saha
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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, Arguello Anahy Santiago   +1 more
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On Some Properties of Addition Signed Cayley Graph ${\mathsf{\Sigma }}_{\mathit{n}}^{\mathbf{\wedge }}$

Mathematics, 2022
We define an addition signed Cayley graph on a unitary addition Cayley graph Gn represented by Σn∧, and study several properties such as balancing, clusterability and sign compatibility of the addition signed Cayley graph Σn∧.
Obaidullah Wardak, Ayushi Dhama, Deepa Sinha   +2 more
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Improved Expansion of Random Cayley Graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2004
In Random Cayley Graphs and Expanders, N. Alon and Y. Roichman proved that for every ε > 0 there is a finite c(ε) such that for any sufficiently large group G, the expected value of the second largest (in absolute value) eigenvalue of the ...
Po-Shen Loh, Leonard J. Schulman
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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
doaj  

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
doaj  

On the degree of the Birkhoff polytope graph [PDF]

Mathematics and Computational Sciences
The 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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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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Orthogonal colourings of Cayley graphs [PDF]

Discrete Mathematics, 2020
Two colourings of a graph are orthogonal if they have the property that when two vertices are coloured with the same colour in one colouring, then those vertices receive distinct colours in the other colouring. In this paper, orthogonal colourings of Cayley graphs are discussed.
Jeannette C. M. Janssen, Kyle MacKeigan
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