On the algebraic connectivity of token graphs
Web5 de out. de 2024 · Algebraic connectivity is one way to quantify graph connectivity, which in turn gauges robustness as a network. In this paper, we consider the problem of maximising algebraic connectivity both local and globally over all simple, undirected, unweighted graphs with a given number of vertices and edges. We pursue this … Web5 de jun. de 2024 · For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that λ2(G)+λ2(G¯) ... A note on the algebraic …
On the algebraic connectivity of token graphs
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Web15 de jan. de 2007 · In Section 2, we also consider the diameter of G and give lower bounds of the Laplacian spectral radius and algebraic connectivity of G involving the diameter. 2. Lower bounds for the Laplacian eigenvalues Let G be a simple connected graph and L (G) = D (G) − A (G) be the Laplacian matrix of G. It is well known that λ n … Webwe say that the connectivity of a graph is optimal. 3 Algebraic connectivity in random graph of Erdos-R˝ ´enyi In this section we give an analytical estimate of the algebraic connectivity in the Erdo˝s-Re´nyi random graph. The analytical estimate relies on the equality with the minimum nodal degree.
Web11 de mai. de 2024 · The -dimensional algebraic connectivity of a graph , introduced by Jordán and Tanigawa, is a quantitative measure of the -dimensional rigidity of that is … Web10 de abr. de 2024 · Bao, Tan and Fan [Y.H. Bao, Y.Y. Tan,Y.Z. Fan, The Laplacian spread of unicyclic graphs, Appl. Math. Lett. 22 (2009) 1011–1015.] characterize the unique …
Web13 de abr. de 2024 · The aim of this note is to revisit the connections between some stochastic games, namely Tug-of-War games, and a class of nonlocal PDEs on graphs. … Webdefined the absolute algebraic connectivity of a graph as the maximum value of λ (L) over all nonnegative edge weights that add up to m, i.e., 1/m times the optimal value of (3). The problem of finding the absolute algebraic connectivity of a graph was discussed in [15, 16], and an analytical solution was presented for tree graphs.
Web25 de mar. de 2024 · The k -token graph F_k (G) of G is the graph whose vertices are the k -subsets of V ( G ), where two vertices are adjacent in F_k (G) whenever their symmetric difference is an edge of G. In 2024 Leaños and Trujillo-Negrete proved that if G is t -connected and t\ge k, then F_k (G) is at least k (t-k+1) -connected.
Web1 de dez. de 2006 · We find an upper bound on the algebraic connectivity of graphs of various genus. We begin by showing that for fixed k ⩾ 1, the graph of genus k of largest … cyndi wang on stageWebPrototype-based Embedding Network for Scene Graph Generation Chaofan Zheng · Xinyu Lyu · Lianli Gao · Bo Dai · Jingkuan Song Efficient Mask Correction for Click-Based … cyndi wherryWeb2 de set. de 2024 · Abstract:We study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The $k$-token … cyndi white omilian facebookWeb11 de mai. de 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. cyndi wang the day you went awayWeb11 de jan. de 2024 · New conjectures on algebraic connectivity and the Laplacian spread of graphs. Wayne Barrett, Emily Evans, H. Tracy Hall, Mark Kempton. We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in a graph. We prove that this lower bound implies a strengthening of … cyndi watson attorneyWeb25 de mar. de 2024 · The k -token graph F_k (G) of G is the graph whose vertices are the k -subsets of V ( G ), where two vertices are adjacent in F_k (G) whenever their … cyndi wearWebThe algebraic connectivity of a graph is one of the most well-studied parameters in spectral graph theory. It is de ned as the second smallest eigenvalue of the … cyndi wheeler myrtle beach