Ars Mathematica ContemporaneaIn this paper, we introduce the concept of $k$-integral graphs. A graph $Γ$ is called $k$-integral if the extension degree of the splitting field of the characteristic polynomial of $Γ$ over rational field $\mathbb Q$ is equal to $k$. We prove that the set of all finite connected graphs with given algebraic degree and maximum degree is finite.
Abdollahi, Alireza +3 more
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Replacement and zig-zag products, Cayley graphs and Lamplighter random walk [PDF]
International Journal of Group Theory, 2013 We investigate two constructions - the replacement and the zig-zag product of graphs - describing several fascinating connections with Combinatorics, via the notion of expander graph, Group Theory, via the notion of semidirect product and Cayley graph ...
Alfredo Donno
doaj
On distance-based topological indices and co-indices of fractal-type molecular graphs and their respective graph entropies. [PDF]
PLoS One, 2023 Malik MA, Imran M, Adeel M.
europepmc +1 more source
NORMAL 6-VALENT CAYLEY GRAPHS OF ABELIAN GROUPS
International Journal of Industrial Engineering and Production Research, 2008 : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6
M. Alaeiyan
doaj
Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups. [PDF]
Commun Math Phys, 2023 Magee M, Thomas J, Zhao Y.
europepmc +1 more source
A Cayley graph for $F_{2}\times F_{2}$ which is not minimally almost convex
We give an example of a Cayley graph $\Gamma$ for the group $F_{2}\times F_{2}$ which is not minimally almost convex (MAC). On the other hand, the standard Cayley graph for $F_{2}\times F_{2}$ does satisfy the falsification by fellow traveler property ...
Price, Andrew Elvey
core
Hamiltonian decompositions of 4-regular Cayley graphs of infinite abelian groups. [PDF]
J Graph Theory, 2022 Erde J, Lehner F.
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Non-Isomorphic Cayley Graphs of Metacyclic Groups of Order 8p with the Same Spectrum
MathematicsThe spectrum of a graph Γ, denoted by Spec(Γ), is the multiset of eigenvalues of its adjacency matrix. A Cayley graph Cay(G,S) of a finite group G is called Cay-DS (Cayley graph determined by its spectrum) if, for any other Cayley graph Cay(G,T), Spec ...
Lang Tang, Weijun Liu, Rongrong Lu
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Relatively dominated representations from eigenvalue gaps and limit maps. [PDF]
Geom Dedic, 2023 Zhu F.
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Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree. [PDF]
Heliyon, 2023 Abu Oun SM, Mallak S, Asad J.
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