графы

Graphs with Contours in Multiresolution Analysis on Vilenkin Groups

Authors: Berdnikov G. S.

The aim of this article is to study the problem of constructing mutiresolution analysis on Vilenkin group. Previous papers by S. F. Lukomskii, Iu. S. Kruss and the author present an algorithm for constructing scaling functions ϕ with compact support, Fourier transform of which also has compact support. The description of such algorithm is tightly connected with directed graphs of special structure, which are constructed with the help of so-called N-valid trees. One of the special properties of these graphs is the absence of directed cycles — contours.

Some Questions on Minimal Extensions of Graphs

Authors: Abrosimov M. B.

Some statements concerning minimal extensions of graphs are presented that seem to be quite evident at first sight but are not so simple under closer inspection.

Minimal vertex 1-extensions of palm trees

Authors: Komarov D. D.

Minimal vertex 1-extension of graphs can be regarded as a model of optimal 1-node fault tolerant implementation of a system. This paper is about of the 1-vertex extensions of a graphs from a special class named palm trees.This article presents a solution to the problem of finding the minimal vertex 1-extension of palm trees with two leafs.