Algebraic Graph Theory

By C. Godsil, Gordon F. Royle. Graduate texts in mathematics, 2001

309 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/b07c157e7d40e06a4f2d486b16d5180d8b24acb9

Citations in the corpus

• Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control (2010, unknown): “We first review some elements of algebraic graph theory (Godsil & Royle, 2001) used in the sequel.”
• Consensus and Cooperation in Networked Multi-Agent Systems (2007, unknown): “Based on analytical tools from algebraic graph theory [23], we later show that x is a unique equilibrium of (2) (up to a constant multiplicative factor) for connected graphs.”
• Decentralized, Adaptive Coverage Control for Networked Robots (2009, unknown): “It is well known (Godsil and Royle 2004) that for a connected graph, the weighted graph Laplacian is positive-semi-definite, L 0, and it has exactly one zero eigenvalue, with the associated eigenvector 1 [1 1]T.”
• Consensus problems in networks of agents with switching topology and time-delays (2004, unknown): “Notice that in Theorem 6, graph does not need to be connected.”
• Chromatic numbers, morphism complexes, and Stiefel-Whitney characteristic classes (2005, unknown): “Shorter proofs were obtained by Bárány, [Bar78], and Greene, [Gr02], both using some versions of the Borsuk-Ulam theorem, see also [GR01].”
• The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, unknown): “In order to scale well with the size of the data, signal processing techniques for graph signals should employ localized operations that compute information about the data at each vertex by using data from a small neighborhood of vertices close to it in the graph.”
• Flocking for multi-agent dynamic systems: algorithms and theory (2006, unknown): “A graph G is a pair ( V , E ) that consists of a set of vertices V = { 1 , 2 . . . , n } and edges E ⊆ { ( i, j ) : i, j ∈ V , j 6 = i } (i.e. the graph is in general directed and has no self-loops).”
• Distributed connectivity control of mobile networks (2007, unknown): “For any graph G, its vertex connectivity, edge connectivity, and second smallest eigenvalue of its Laplacian matrix satisfy λ2(L(G)) ≤ κ(G) ≤ η(G) [28].”
• Mathematical Formulation of Multilayer Networks (2013, unknown): “In particular, the overlay network ignores the non-negligible contribution of inter-layer connections, which are also important for quantifying the properties of a multi-layer network.”