Integral cayley graphs over abelian groups
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] Nettet1. apr. 2024 · The following result provides a simple criterion for integral Cayley graphs over an abelian group G by using the integral sets and atoms of B (G). Theorem 2.4 …
Integral cayley graphs over abelian groups
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Nettet30. mar. 2024 · Based on the representation theory of finite groups, we first show that an abelian Cayley graph is integral if and only if it is distance-integral, which naturally contains a main result obtained in [Electron. J. Comb. 19(4) (2012) paper 25, 8 pp]. NettetThe eigenvalues of A will be referred to as the eigenvalues or the spectra of the graphΓ.A graph is named an integral graph if all its eigenvalues are integers. Suppose that G is …
Nettet15. feb. 2024 · Now we can present a characterization on periodicity of integral connected abelian Cayley graphs. Let Γ be such a graph. Since Γ is integral, αx∈Zfor all x∈G. We define(7)M=gcd(d−αx:x∈G)(d= S )where d−αx=d−∑g∈Sχx(g)≥0and d−α0=0. For any x∈G, if d−αx=0then χx(g)=1for all g∈S. NettetPerfect state transfer on weighted bi-Cayley graphs over abelian groups☆. Author links open overlay panel Shixin Wang, Tao Feng. Show more
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 … 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. 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.
NettetWe de ne quasi-abelian n-Cayley graphs in analogous way to quasi-abelian Cayley graphs as follows. Definition 1.1. Cay(G;T ij j1 i;j n) is called a quasi-abelian n-Cayley graph if for all 1 i;j n, T ij’s are unions of conjugacy classes of G. The characteristic polynomial of an n-Cayley graph over a group Gis determined h\u0026m rumiaNettet25. 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 … autos valle vwNettet1. 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 … h\u0026m opening times sundayNettet28. 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. autos vanrellNettet1. 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 … h\u0026m romania barbatiNettetIn the mathematics of Sudoku, the Sudoku graph is an undirected graph whose vertices represent the cells of a (blank) Sudoku puzzle and whose edges represent pairs of cells that belong to the same row, column, or block of the puzzle. The problem of solving a Sudoku puzzle can be represented as precoloring extension on this graph. It is an … autos valle san pedroNettet17. 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 … autos vanilla gta 5