Eigenvalues of neutral networks: interpolating between hypercubes
| Autor: | T. Reeves, Robert Farr, Thomas M. A. Fink, Jamie R. Blundell, A. Gallagher |
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| Rok vydání: | 2015 |
| Předmět: |
0301 basic medicine
Discrete mathematics 0102 computer and information sciences 01 natural sciences Theoretical Computer Science Hypercube graph Combinatorics Mathematics - Spectral Theory 03 medical and health sciences Indifference graph 030104 developmental biology Hamming graph 010201 computation theory & mathematics Chordal graph FOS: Mathematics Discrete Mathematics and Combinatorics Hypercube Adjacency matrix Spectral Theory (math.SP) Eigenvalues and eigenvectors Mathematics Universal graph |
| DOI: | 10.48550/arxiv.1504.03065 |
| Popis: | A neutral network is a subgraph of a Hamming graph, and its principal eigenvalue determines its robustness: the ability of a population evolving on it to withstand errors. Here we consider the most robust small neutral networks: the graphs that interpolate pointwise between hypercube graphs of consecutive dimension (the point, line, line and point in the square, square, square and point in the cube, and so on). We prove that the principal eigenvalue of the adjacency matrix of these graphs is bounded by the logarithm of the number of vertices, and we conjecture an analogous result for Hamming graphs of alphabet size greater than two. |
| Databáze: | OpenAIRE |
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