Walter Julio Cortez MORALES[1]

§     ABSTRACT: In this paper we define the extension and quasi-inverse graphs of the arbitrary G, which associate to each vertex of Gwith a clique-2. The extension graph generalizes a useful vertex-splitting notion of Tutte for simple graphs. This transformation is a kind of inverse of edge contraction. From two new graphs above mentioned, we introduce the notion of quasi-homeomorphism in arbitrary graphs. The main result of this work is to prove that wheel and bouquet graphs are quasi-homeomorphisms. Moreover, we give a condition for an extension graph to be quasi-inverse of G.

§     KEYWORDS: Graph; clique-2; quasi-inverse; quasi-homeomorphism; extension.


[1] Departamento de Ciências de Computação e Estatística, Universidade Estadual Paulista – UNESP, São José do Rio Preto, São Paulo, Brasil. E-mail: walter@ibilce.unesp.br