Integral cayley graphs over abelian groups

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August undefined, 2024

NettetIf Y is a walk regular graph and X is an abelian 2ev-cover of Y then X is walk regular. Proof. The regular representation of the abelian group G = H1 × H2 is the tensor product of the regular representations of H1 and H2 . Hence for each g ∈ G we have ρ(g) = ρH1 (h1 ) ⊗ ρH2 (h P2 ), and ρ(g) still has zero diagonal unless g = id. Nettet1. jun. 2024 · In fact, Cayley graphs over abelian groups are integral if and only if they are distance integral, as shown by Huang–Li [9]. Moreover, the same authors [10] got sufficient conditions for the equivalence between the integrality and the distance integrality of Cayley graphs over generalized dihedral groups.

State transfer on integral mixed circulant graphs

NettetPerfect state transfer on weighted bi-Cayley graphs over abelian groups☆. Author links open overlay panel Shixin Wang, Tao Feng. Show more Nettet31. des. 2024 · Let be an abelian group. We characterize the set for which a mixed Cayley graph is HS-integral. We also show that a mixed Cayley graph is Eisenstein … refrigeration calculation formula

Algebraic degree of Cayley graphs over abelian groups and …

Nettet[1] This graph is the Cayley graph of an abelian group. Among abelian Cayley graphs that are strongly regular and have the last two parameters differing by one, it is the only graph that is not a Paley graph. [2] It is also an integral graph, meaning that the eigenvalues of its adjacency matrix are integers. [3] http://www.vesnik.math.rs/vol/mv20407.pdf NettetPerfect state transfer on weighted bi-Cayley graphs over abelian groups☆. Author links open overlay panel Shixin Wang, Tao Feng. Show more refrigeration cabinet manufacturers

Perfect State Transfer on Cayley graphs over finite abelian groups

Perfect state transfer on weighted bi-Cayley graphs over abelian groups ...

Nettetabelian groups in general. This can be conﬁrmed for cyclic groups by a theorem of So [16]. In Section 3 we extend the result of So to gcd-groups. A Cayley graph Cay(Γ,S) over a gcd-group Γ is integral, if and only if S∈ B(Γ). 2 gcd-Groups Throughout this section Γ denotes a ﬁnite abelian group given as a direct product of cyclic groups, Nettet15. jul. 2024 · On the same year, Klotz and Sander [21] proved that if a Cayley graph Cay (Γ, S) over an abelian group Γ is integral then S belongs to the Boolean algebra B (Γ) … refrigeration capsule packNettetIn this paper, we focus on the dihedral groups and the dicyclic groups, and consider their corresponding integral Cayley graphs. We obtain the sufficient conditions for the … refrigeration career

"Nettet25. sep. 2009 · In the same year, Klotz and Sander [10] proved that if the Cayley graph Cay(Γ, S) over abelian group Γ is integral, then S belongs to the Boolean algebra … " - Integral cayley graphs over abelian groups

Integral cayley graphs over abelian groups

Perfect State Transfer on Weighted Abelian Cayley Graphs*

Nettet1. jun. 2024 · In fact, Cayley graphs over abelian groups are integral if and only if they are distance integral, as shown by Huang–Li [9]. Moreover, the same authors [10] got … Nettet17. des. 2024 · Cayley graphs over abelian groups, H-integral normal Cayley graphs and HS-integral mixed circulant graphs have been characterized in [18], [17], [16] and …

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Nettet31. aug. 2024 · By Theorem 3.3, X (D_7,S) is not integral. Although the integral Cayley graphs over dihedral groups are completely characterized by Theorem 3.3, it seems … Nettet18. nov. 2024 · In this paper, we completely determine the algebraic degrees of Cayley graphs over abelian groups and dihedral groups. 1 Introduction The algebraic …

NettetCayley graphs over symmetric groups are integral (a Cayley graph is said to be normal if its generating set S is closed under conjugation). It seems that there are few works about the characterization of integral Cayley graphs over non-abelian groups. As a simple attempt to this aspect, we try to characterize integral Cayley graphs over ... NettetTamon [1] asked for a complete characterization of integral circulant graphs admitting PST. Based on So’s characterization [24] for integral circulant graphs, Ba si c [3] gave an answer to this question. Very recently, Arnad ottir and Godsil [ 2] characterized PST on Cayley graphs for abelian groups that have a cyclic Sylow-2-subgroup, which ...

Nettet16. nov. 2024 · Integral Cayley Graphs. Let G be a group and S ⊆ G a subset such that S = S−1, where S−1 = { s−1 s ∈ S }. Then a Cayley graph Cay ( G, S) is an undirected … Nettet1. des. 2024 · A finite abelian group G is called Cayley sum integral if for any subgroup H of G all Cayley sum graphs on H are integral. In this paper, the classes A2 and A3 …

Nettet28. jan. 2016 · We find that if a Cayley graph over a finite abelian group exhibits perfect state transfer then it must have integral spectrum. A gcd-graph is a Cayley graph over a finite abelian group defined by greatest common divisors. It is well known that all gcd-graphs have integral spectrum.

NettetA graph is called integral, if all of its eigenvalues are integers. For an abelian group Î we show that Cay(Î ,S) is integral, if S belongs to the Boolean algebra B(Î ) generated by the subgroups of Î . The converse is proven for cyclic groups. A finite group Î is called Cayley integral, if every undirected Cayley graph over Î is integral. refrigeration capillary tubeNettet13. feb. 2024 · Abdollahi and Vatandoost [1; 2], determined integral cubic and tetravalent Cayley graphs on abelian groups. By using a result of Babai which presented the … refrigeration capacityNettetFix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multiplication. Any subg… refrigeration certification long beach