On the distance eigenvalues of cayley graphs

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August undefined, 2024

Web30 de mar. de 2024 · Abstract. A graph is said to be distance-integral if every eigenvalue … WebAlso we prove that a nite abelian group G admits a connected cubic distance integral Cayley graph if and only if G is isomorphic to one of the groups Z_4, Z_6, Z_4 xZ_2, Z_6 xZ_2, or Z_2 x Z_2 xZ_2. Furthermore, up to isomorphism, there are exactly 5 connected cubic distance integral Cayley graphs over abelian groups.

[PDF] Eigenvalues of Cayley Graphs Semantic Scholar

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. Web10 de nov. de 2024 · The eigenvalues of this matrix, together with their multiplicities, are an important invariant of the graph. Since A is symmetric, all eigenvalues are real. For a regular graph of degree d, it is well-known that the largest eigenvalue of A is \lambda _ … how get microsoft points

Vertex-transitive graph - Wikipedia

WebOn the other hand, we show that every n-vertex Cayley graph (and more generally, vertex-transitive graph) has an orthonormal basis whose coordinates are all O(p logn=n), and that this boundisnearlybestpossible. Our investigation is motivated by a question of Assaf Naor, who proved that random abelian Webon 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. Web4 de out. de 2024 · A graph Γ is called an n-Cayley graph over a group G if Aut (Γ) … how get money for free

The Distance Spectra of Cayley Graphs of Coxeter Groups

Web20 de out. de 2016 · Let G be a graph and let diam(G) denote the diameter of G.The distance power G N of G is the undirected graph with vertex set V(G), in which x and y are adjacent if their distance d(x, y) in G belongs to N, where N is a non-empty subset of {1, 2, …, diam (G)}.The unitary Cayley graph is the graph having the vertex set Z n and the … WebIn this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. how get mods minecraftWeb4 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. highest fiber breakfast food

"WebThe Kuramoto model of coupled phase oscillators on complete, Paley, and Erdős-Rényi (ER) graphs is analyzed in this work. As quasirandom graphs, the complete, Paley, and ER graphs share many structural properties. For … " - On the distance eigenvalues of cayley graphs

On the distance eigenvalues of cayley graphs

Upper bounds for Steklov eigenvalues of subgraphs of polynomial …

Web13 de out. de 2016 · We consider quasirandom properties for Cayley graphs of finite … Web26 de set. de 2024 · Download a PDF of the paper titled Eigenvalues of Cayley graphs, …

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Web1 de jun. de 2024 · 5.1. Main result. The next theorem, which characterizes distance … Web6 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 …

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 … Web1 de fev. de 2015 · On the eigenvalues of normal edge-transitive Cayley graphs …

Web26 de set. de 2024 · We survey some of the known results on eigenvalues of Cayley … WebGraph covers with two new eigenvalues Chris Godsil∗1 , Maxwell Levit†1 , and Olha Silina†1 arXiv:2003.01221v3 [math.CO] 7 Oct 2024 1 Department of Combinatorics & Optimization, University of Waterloo October 7, 2024 Abstract A certain signed adjacency matrix of the hypercube, which Hao Huang used last year to resolve the Sensitivity …

Web1 de jan. de 2024 · Let G be a connected threshold graph. Then each distance eigenvalue λ D ≠ − 1, − 2 of G is simple, and G has no distance eigenvalues in the interval (− 2, − 1). Motivated by the works of Ghorbani [10] and Lu, Huang and Lou [24], in this paper, we study the multiplicity and the distribution of distance eigenvalues of cographs. Theorem 1.2

how get microsoft word freeWebEigenvalues of graphs and digraphs. Chris Godsil. 1982, Linear Algebra and its … how get money online for freeWebDOI: 10.1080/03081087.2024.1758609 Corpus ID: 219046404; Distance powers of integral Cayley graphs over dihedral groups and dicyclic groups @article{Cheng2024DistancePO, title={Distance powers of integral Cayley graphs over dihedral groups and dicyclic groups}, author={Tao Cheng and Lihua Feng and Weijun Liu and Lu Lu and Dragan … how get microsoft edgeWeb1 de mar. de 2014 · We establish a relation between the eigenvalues of the arrangement graphs and the eigenvalues of certain Cayley graphs. As a result, the conjecture on integrality of eigenvalues of A (n, k, 1 ... The distance spectra of Cayley graphs of Coxeter groups. Discrete Math., 311 (2011), pp. 738-755. Article. Download PDF View … how get medicare cardhttp://www.vesnik.math.rs/vol/mv20407.pdf how get military discount online amc theatresWebother 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 ... how get microsoft action packWebThe 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 get microsoft office