On the distance eigenvalues of cayley graphs

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Web1 de jul. de 2024 · We express the discrete Ricci curvature of a graph as the minimal eigenvalue of a family of matrices, one for each vertex of a graph whose entries depend on the local adjaciency structure of the graph. Using this method we compute or bound the Ricci curvature of Cayley graphs of finite Coxeter groups and affine Weyl groups. Web26 de set. de 2024 · Download a PDF of the paper titled Eigenvalues of Cayley graphs, …

Cayley graph - Encyclopedia of Mathematics

WebIn mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, … how to show google chrome icon on home page

Distance-regular Cayley graphs with least eigenvalue - Springer

WebLet $\Gamma$ be an antipodal distance-regular graph with diameter $4$ and eigenvalues ... It is shown that every finite group has a connected normal bi-Cayley graph and improves ... Second largest eigenvalue 5. Other eigenvalues of the adjacency matrix 6. Laplacian eigenvalues 7. Signless Laplacian eigenvalues 8. … Expand. 56. Save. Alert. Web1 de out. de 2024 · Assume that Γ = Cay (G, S) is a primitive distance-regular Cayley … WebThe Cayley tree has been widely used in solid state and statistical physics, as statistical mechanical models on it form a large class of exactly soluble models.[27,28]We find that the fidelity of the final state of the system and the target state in both the CTQW and the typical DTQW approach is less than unitary by analyzing the evolutionary process on the … how to show google drive on desktop

The Distance Spectra of Cayley Graphs of Coxeter Groups

Vertex-transitive graph - Wikipedia

Web26 de set. de 2024 · Abstract: We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs. Subjects: Combinatorics (math.CO) MSC classes: 05C50, 05C25: Cite as: Web1 de jan. de 2024 · For the results on the distance eigenvalues of cographs, Lu, Huang … nottinghamshire apprenticeshipsWebThis lecture is devoted to an examination of some special graphs and their eigenvalues. 5.2 The Ring Graph The ring graph on nvertices, R n, may be viewed as having a vertex set corresponding to the integers modulo n. In this case, we view the vertices as the numbers 0 through n 1, with edges (i;i+ 1), computed modulo n. Lemma 5.2.1. The ... how to show google calendar in gmail

"WebWe prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with … " - On the distance eigenvalues of cayley graphs

On the distance eigenvalues of cayley graphs

Web20 de out. de 2016 · Let G be a graph and let diam(G) denote the diameter of G.The … Web26 de set. de 2024 · We survey some of the known results on eigenvalues of Cayley …

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WebWe also obtain distance Laplacian eigenvalues and distance LaplacianenergyofGn. Keywords: Spectrum; Energy; Signless Laplacian; Distance Laplacian; Distance signless Laplacian; Unitary Cayley graph; Unitary addition Cayley graph 1 Introduction Let G be a simple, undirected graph of order n and size m with vertex set V(G) and edge set E(G). Webother Cayley graph on S n that arises in extremal combinatorics [17, 32] is the derangement graph ( S n;f˙2S n: ˙(i) 6=i;i2[n]g). The adjacency spectra of these graphs (the eigenvalues of their adjacency matrices) are of interest for their own sake, as well as for various applications such as card shu ing (random walks on the symmetric group ...

Web30 de mar. de 2024 · A graph is called distance integral if all of its distance eigenvalues are integers. In this paper, we introduce some new classes of distance integral graphs. In particular, we show that if n, k ... WebIn the literature, the adjacency eigenvalues of Cayley graphs have been more widely used than the distance eigenvalues. A graph Γ is called distance (adjacency) integral if all the eigenvalues of its distance (adjacency) matrix are integers. A graph is called circulant if it is a Cayley graph over a cyclic group.

Web4 de jul. de 2024 · where C i is a conjugacy class in a finite group G. Suppose S is symmetric; that is, x ∈ S implies x − 1 ∈ S. Consider the Cayley graph X ( G, S). Show that the eigenvalues of the adjacency matrix of this graph have the form λ π = 1 d π ∑ s ∈ S χ π ( s), where π ∈ G ^, and d π = the degree of π. WebIn the mathematical field of graph theory, a vertex-transitive graph is a graph G in which, given any two vertices v 1 and v 2 of G, there is some automorphism: such that =. In other words, a graph is vertex-transitive if its automorphism group acts transitively on its vertices. A graph is vertex-transitive if and only if its graph complement is, since the group …

WebWe consider resonance in cata-condensed benzenoids having six and seven fused benzene rings. The resonance relationship between the Kekule valence structures of the molecules is represented by the resonance graphs in which the vertices represent the Kekule valence structures, and the edges, the presence of the quantum chemical resonance integral …

WebEigenvalues of graphs and digraphs. Chris Godsil. 1982, Linear Algebra and its Applications ... nottinghamshire apxWeb4 de out. de 2024 · A graph Γ is called an n-Cayley graph over a group G if Aut (Γ) … how to show google photos on samsung tvWeb30 de mar. de 2024 · A graph is called distance integral if all of its distance … how to show google map in androidWeb6 de set. de 2024 · It is therefore natural to wonder whether it is possible to extend our control to all of the eigenvalues of a subgraph of any polynomial growth Cayley graph. The main result of this paper is the following: Theorem 5. Let $\Gamma = Cay(G,S)$ be a polynomial growth Cayley graph of order $d \ge 2$. Let $(\Omega , B)$ be a subgraph … how to show google on home screenWebon the structure of distance-regular Cayley line graphs of incidence graphs of generalized polygons. Keywords Cayley graph · Strongly regular graph · Distance-regular graph · Line graph · Generalized polygon · Eigenvalues Mathematics Subject Classiﬁcation 05E30 · 05C25 · 20D60 · 51E12 In honor of Andries Brouwer for his 65th birthday. how to show google icon on desktopWeb30 de mar. de 2024 · Abstract. A graph is said to be distance-integral if every eigenvalue … nottinghamshire apprenticeships log inWebOf special interest is the case for directed Cayley graphs whose vertex set is a group Γ and the directed edges are generated by a subset B of elements of Γ as f(x;bx):x2Γ;b2Bg. For a directed Cayley graph, the condition of strong connectivity is equivalent to the assumption that B is a generating set. how to show grand total in matrix in power bi