On Upper Bounds for Minimum Distance and Covering Radiusof Non-binary Codes
Designs, Codes and Cryptography
Bounds on Special Subsets in Graphs, Eigenvalues and Association Schemes
Journal of Algebraic Combinatorics: An International Journal
On spectral bounds for cutsets
Discrete Mathematics
A General Spectral Bound for Distant Vertex Subsets
Combinatorics, Probability and Computing
The Laplacian spectral radius of a graph under perturbation
Computers & Mathematics with Applications
Laplacian spectral bounds for clique and independence numbers of graphs
Journal of Combinatorial Theory Series B
High-ordered random walks and generalized laplacians on hypergraphs
WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
Differentially private iterative synchronous consensus
Proceedings of the 2012 ACM workshop on Privacy in the electronic society
Loose laplacian spectra of random hypergraphs
Random Structures & Algorithms
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The authors give a new upper bound for the diameter $D(G)$ of a graph $G$ in terms of the eigenvalue of the Laplacian of $G$. The bound is $$ D(G)\leqq \lfloor\fract{cosh^{-1}(n-1)}{cosh^{-1}\frac{\lambda_n + \lambda_2}{\lambda_n - \lambda_2}}\rfloor +1, $$ where $0\leq \lambda_2 \leq \cdots \leq \lambda_n$ are the eigenvalues of the Laplacian of $G$ and where $\lfloor \rfloor$ is the floor function.