Authors: Flavia Bonomo ^1,2; Celina M. H. Figueiredo ³; Guillermo Duran ^4,5,6,7; Luciano N. Grippo ⁸; Martín D. Safe ⁸; Jayme L. Szwarcfiter ^3,9

• 1 Departamento de Computación [Buenos Aires]
• 2 Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
• 3 Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia
• 4 Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
• 5 Departamento de Matemática [Buenos Aires]
• 6 Departamento de Ingenieria Industrial [Santiago]
• 7 Instituto de Cálculo [Buenos Aires]
• 8 Instituto de Ciencias [Los Polvorines]
• 9 Nucleo de Computação Eletrônica

Given a class G of graphs, probe G graphs are defined as follows. A graph G is probe G if there exists a partition of its vertices into a set of probe vertices and a stable set of nonprobe vertices in such a way that non-edges of G, whose endpoints are nonprobe vertices, can be added so that the resulting graph belongs to G. We investigate probe 2-clique graphs and probe diamond-free graphs. For probe 2-clique graphs, we present a polynomial-time recognition algorithm. Probe diamond-free graphs are characterized by minimal forbidden induced subgraphs. As a by-product, it is proved that the class of probe block graphs is the intersection between the classes of chordal graphs and probe diamond-free graphs.