Constructions for type I trees with nonisomorphic Perron branches

Stephen J. Kirkland

On a bound on algebraic connectivity: the case of equality

Stephen J. Kirkland, Neumann, Michael, Bryan L. Shader (1998)

Czechoslovak Mathematical Journal

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In a recent paper the authors proposed a lower bound on $1 - λ_{i}$ , where $λ_{i}$ , $λ_{i} \neq 1$ , is an eigenvalue of a transition matrix $T$ of an ergodic Markov chain. The bound, which involved the group inverse of $I - T$ , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in...

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