The bottleneck matrix M of a rooted tree T is combinatorial object encoding the spatial distribution vertices with respect to root. spectral radius M, known as Perron value tree, closely related theory algebraic connectivity. In this paper, we investigate values various classes trees by making use and linear-algebraic techniques. This results in multiple bounds on these classes, which can be st...

We consider subshifts of nite type on the symbol space generated by incidence matrices over a countably innnite alphabet. We extend the deenition of topological pressure to this context and, as our main result, we construct a new class of Gibbs states of HH older continuous potentials on these symbol spaces. We establish some basic stochastic properties of these Gibbs states: exponential decay ...

It is shown that the upper and lower Henstock integrals coincide with upper and lower Perron integrals, when the former exist.