On the algebraic connectivity of token graphs
WebThis paper introduces token graphs and studies some of their properties including: connectivity, diameter, cliques, chromatic number, Hamiltonian paths, and Cartesian … 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 …
On the algebraic connectivity of token graphs
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WebThe algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other words, it is the second smallest root of the graph's Laplacian polynomial. This eigenvalue is greater than 0 iff G is a connected graph. The ratio of the Laplacian spectral radius to … Web25 de jul. de 2024 · Some Background. The algebraic connectivity of a graph G is defined as the second smallest Laplacian eigenvalue of the graph and is denoted by a ( G). It is known that a ( G) ≤ 1 if G is a tree and in particular, when the tree is a star then equality holds. Further, if G is a complete graph, then a ( G) = n where n is the number of …
Web19 de jun. de 2024 · In 2012 Fabila-Monroy et al. reintroduced the concept of k-token graph as “a model in which k indistinguishable tokens move from vertex to vertex along the … WebPrototype-based Embedding Network for Scene Graph Generation Chaofan Zheng · Xinyu Lyu · Lianli Gao · Bo Dai · Jingkuan Song Efficient Mask Correction for Click-Based …
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. 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 …
WebWe study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The k-token graph F k(G) of a graph Gis the …
Web11 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. high-speed interfaceWebThe properties of token graphs have been studied since 1991 by various authors and with different names, see, e.g., [1,2,3,5,9] and, in recent years, the study of its combinatorial properties and ... high-speed key encapsulation from ntruWebwith them. The first major section of this paper is a survey of key results in Spectral Graph Theory. There are fascinating results involving the connectivity, spanning trees, and a … small lightweight bagless vacuum cleanersWebwe 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. high-speed integrated qkd systemWeb11 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 … high-speed downstream channelWeb13 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. … small lightweight backpack for waterWeb1 de out. de 2015 · We study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The k -token graph F k ( G ) … small lightweight canoes