Superconnectivity of graphs with odd girth g and even girth h

Authors:
C. Balbuena;P. García-Vázquez;L. P. Montejano
Affiliations:
Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Campus Nord, Edifici C2, C/ Jordi Girona 1 i 3, E-08034 Barcelona, Spain;Departamento de Matemática Aplicada I, Universidad de Sevilla, Av. Reina Mercedes s/n, Sevilla, Spain;Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Campus Nord, Edifici C2, C/ Jordi Girona 1 i 3, E-08034 Barcelona, Spain
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

A maximally connected graph of minimum degree @d is said to be superconnected (for short super-@k) if all disconnecting sets of cardinality @d are the neighborhood of some vertex of degree @d. Sufficient conditions on the diameter to guarantee that a graph of odd girth g and even girth h=g+3 is super-@k are stated. Also polarity graphs are shown to be super-@k.