The minimal spectral radius of graphs with a given diameter

  title={The minimal spectral radius of graphs with a given diameter},
  author={Edwin R. van Dam and Robert E. Kooij},
The spectral radius of a graph (i.e., the largest eigenvalue of its corresponding adjacency matrix) plays an important role in modeling virus propagation in networks. In fact, the smaller the spectral radius, the larger the robustness of a network against the spread of viruses. Among all connected graphs on n nodes the path Pn has minimal spectral radius. However, its diameter D, i.e., the maximum number of hops between any pair of nodes in the graph, is the largest possible, namely D = n − 1… CONTINUE READING


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