Про структуру 9-ти вершинних графів-обструкцій для поверхні Клейна

Abstract

В роботі встановлені методом φ-перетворення графів структурні властивості 9-ти вершинних графів-обструкцій для поверхні неорієнтованого роду 2.The structure of the 9 vertex obstructive graphs for the nonorientable surface of the genus 2 is established by the method of φ-transformations of the graphs. The problem of establishing the structural properties of 9 vertex obstruction graphs for the surface of the undirected genus 2 by the method of -transformation of graphs is considered. The article has an introduction and 5 sections. The introduction contains the main definitions, which are illustrated, to some extent, in Section 1, which provides several statements about their properties. Sections 2 – 4 investigate the structural properties of 9 vertex obstruction graphs for an undirected surface by presenting as a -image of several graphs homeomorphic to one of the Kuratovsky graphs and at least one pla-nar or projective-planar graph. Section 5 contains a new version of the proof of the statement about the peculi-arities of the minimal embeddings of finite graphs in nonorientable surfaces, namely, that, in contrast to oriented surfaces, cell boundaries do not contain repeated edges.