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JCT
2007
119views more  JCT 2007»
13 years 6 months ago
Cliques and the spectral radius
We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue (G) of its adjacency matrix. In particular, writing ks (G) for the number of s...
Béla Bollobás, Vladimir Nikiforov
CPC
2006
92views more  CPC 2006»
13 years 6 months ago
Waiting for a Bat to Fly By (in Polynomial Time)
We observe returns of a simple random walk on a finite graph to a fixed node, and would like to infer properties of the graph, in particular properties of the spectrum of the trans...
Itai Benjamini, Gady Kozma, László L...
WG
2004
Springer
14 years 1 days ago
Unhooking Circulant Graphs: A Combinatorial Method for Counting Spanning Trees and Other Parameters
It has long been known that the number of spanning trees in circulant graphs with fixed jumps and n nodes satisfies a recurrence relation in n. The proof of this fact was algebra...
Mordecai J. Golin, Yiu-Cho Leung
CDC
2010
IEEE
142views Control Systems» more  CDC 2010»
13 years 1 months ago
Consensus with constrained convergence rate: Agreement in communities
The study focuses on a class of discrete-time multi-agent systems modelling opinion dynamics with decaying confidence. Essentially, we propose an agreement protocol that impose a p...
Constantin-Irinel Morarescu, Antoine Girard
JCT
2008
85views more  JCT 2008»
13 years 6 months ago
Smith normal form and Laplacians
Let M denote the Laplacian matrix of a graph G. Associated with G is a finite group (G), obtained from the Smith normal form of M, and whose order is the number of spanning trees o...
Dino J. Lorenzini