In this paper, we determine graphs with the largest spectral radius among all the tricyclic graphs with n vertices and k pendent vertices. © 2008 Elsevier Inc. All rights reserved. AMS classification: 05C50; 05C35

We suggest an approach for finding the maximal and the minimal spectral radius of linear operators from a given compact family of operators, which share a common invariant cone (e.g. family of nonnegative matrices). In the case of families with so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and for finding the joint and lower spectral radii of...

A b s t r a c t. Let K3 and K ′ 3 be two complete graphs of order 3 with disjoint vertex sets. Let B∗ n(0) be the 5-vertex graph, obtained by identifying a vertex of K3 with a vertex of K ′ 3 . Let B∗∗ n (0) be the 4-vertex graph, obtained by identifying two vertices of K3 each with a vertex of K ′ 3 . Let B∗ n(k) be graph of order n , obtained by attaching k paths of almost equal length to the...

For n ≥ 2 and a local field K, let ∆n denote the affine building naturally associated to the symplectic group Spn(K). We compute the spectral radius of the subgraph Yn of ∆n induced by the special vertices in ∆n, from which it follows that Yn is an analogue of a family of expanders and is non-amenable.

For n ≥ 2 and a local field K, let ∆n denote the affine building naturally associated to the symplectic group Spn(K). We compute the spectral radius of the subgraph Yn of ∆n induced by the special vertices in ∆n, from which it follows that Yn is an analogue of a family of expanders and is non-amenable.

The largest eigenvalue of the adjacency matrix of a network (referred to as the spectral radius) is an important metric in its own right. Further, for several models of epidemic spread on networks (e.g., the ‘flu-like’ SIS model), it has been shown that an epidemic dies out quickly if the spectral radius of the graph is below a certain threshold that depends on the model parameters. This motiva...