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Algebraic approach to locally finite trees with one end

Bohdan Zelinka (2003)

Mathematica Bohemica

Let T be an infinite locally finite tree. We say that T has exactly one end, if in T any two one-way infinite paths have a common rest (infinite subpath). The paper describes the structure of such trees and tries to formalize it by algebraic means, namely by means of acyclic monounary algebras or tree semilattices. In these algebraic structures the homomorpisms and direct products are considered and investigated with the aim of showing, whether they give algebras with the required properties. At...

Algebraic conditions for t -tough graphs

Bo Lian Liu, Siyuan Chen (2010)

Czechoslovak Mathematical Journal

We give some algebraic conditions for t -tough graphs in terms of the Laplacian eigenvalues and adjacency eigenvalues of graphs.

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