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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.

Algebraic connectivity of k -connected graphs

Stephen J. Kirkland, Israel Rocha, Vilmar Trevisan (2015)

Czechoslovak Mathematical Journal

Let G be a k -connected graph with k ≥ 2 . A hinge is a subset of k vertices whose deletion from G yields a disconnected graph. We consider the algebraic connectivity and Fiedler vectors of such graphs, paying special attention to the signs of the entries in Fiedler vectors corresponding to vertices in a hinge, and to vertices in the connected components at a hinge. The results extend those in Fiedler’s papers Algebraic connectivity of graphs (1973), A property of eigenvectors of nonnegative symmetric...

Algebraic tools for the construction of colored flows with boundary constraints

Marius Dorkenoo, Marie-Christine Eglin-Leclerc, Eric Rémila (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We give a linear time algorithm which, given a simply connected figure of the plane divided into cells, whose boundary is crossed by some colored inputs and outputs, produces non-intersecting directed flow lines which match inputs and outputs according to the colors, in such a way that each edge of any cell is crossed by at most one line. The main tool is the notion of height function, previously introduced for tilings. It appears as an extension of the notion of potential of a flow in a planar...

Algebraic tools for the construction of colored flows with boundary constraints

Marius Dorkenoo, Marie-Christine Eglin-Leclerc, Eric Rémila (2010)

RAIRO - Theoretical Informatics and Applications

We give a linear time algorithm which, given a simply connected figure of the plane divided into cells, whose boundary is crossed by some colored inputs and outputs, produces non-intersecting directed flow lines which match inputs and outputs according to the colors, in such a way that each edge of any cell is crossed by at most one line. The main tool is the notion of height function, previously introduced for tilings. It appears as an extension of the notion of potential of a flow in...

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