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Integral cayley graphs over abelian groups

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 … 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].

Pretty good state transfer on Cayley graphs over dihedral groups

Nettetdetermine the splitting fields and algebraic degrees of mixed Cayley graphs over abelian groups. This generalizes the main results of [K. M¨onius, Splitting fields of spectra of circulant graphs, J. Algebra 594(15) (2024) 154–169] and [M. Kadyan, B. Bhattacharjya, Integral mixed Cayley graphs over abelian groups, Electron. J. Nettet5. apr. 2024 · Lambda Seminars # The Lambda seminar meets approximately once every two weeks, and its main objectives are to allow doctoral students to present both their research topic and any other topic they like, and to do so in a relaxed and probably less stressful environment than that of a first major conference. allow doctoral students in … mario cuomo bridge location https://zappysdc.com

Integral Cayley multigraphs over Abelian and Hamiltonian groups

Nettet30. jul. 2024 · A method to determine algebraically integral Cayley digraphs on finite abelian group arXiv Authors: Fei Li Anhui University of Finance and Economics … NettetIn 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 … Nettet12. apr. 2024 · manuscripta mathematica - For an abelian surface of Picard number 1, we shall study birational automorphims and automorphisms of a generalized Kummer manifold. damon cusato

Distance-integral Cayley graphs over abelian groups and …

Category:Distance powers of integral Cayley graphs over dihedral …

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Integral cayley graphs over abelian groups

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

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 … Nettet20. des. 2010 · For an abelian group Γ we show that Cay (Γ,S) is integral, if S belongs to the Boolean algebra B (Γ) generated by the subgroups of Γ. The converse is proven for …

Integral cayley graphs over abelian groups

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NettetBecause of the good algebraic properties of Cayley graphs, group representations were employed to study perfect state transfer on Cayley graphs over abelian groups [23], … 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 …

NettetWe first classify all finite groups that have a nontrivial Cayley graph with integer eigenvalues, thus solving a problem proposed by Abdollahi and Jazaeri. The notion of … NettetSoluciona tus problemas matemáticos con nuestro solucionador matemático gratuito, que incluye soluciones paso a paso. Nuestro solucionador matemático admite matemáticas básicas, pre-álgebra, álgebra, trigonometría, cálculo y mucho más.

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 … 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 …

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NettetPerfect state transfer on weighted bi-Cayley graphs over abelian groups☆. Author links open overlay panel Shixin Wang, Tao Feng. Show more mario cuomo children imagesNettet16. 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 … mario cuomo siblingsNettet15. 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. mario cuomo relation to andrew cuomoNettetTamon [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 ... mario cuomo still aliveNettetWe 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 mario cuomo bridge traffic todayNettet1. 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 … mario cuomo heightNettet25. mai 2010 · Integral Cayley Graphs over Abelian Groups @article{Klotz2010IntegralCG, title={Integral Cayley Graphs over Abelian Groups}, … mario cupelli