On the connectivity and superconnected graphs with small diameter

Authors:
C. Balbuena;K. Marshall;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;School of Electrical Engineering and Computer Sciences, The University of Newcastle, University Drive, Callaghan NSW 2308, Australia;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:
2010

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Abstract

In this paper, first we prove that any graph G is 2-connected if diam(G)@?g-1 for even girth g, and for odd girth g and maximum degree @D@?2@d-1 where @d is the minimum degree. Moreover, we prove that any graph G of diameter diam(G)@?g-2 satisfies that (i) G is 5-connected for even girth g and @D@?2@d-5, and (ii) G is super-@k for odd girth g and @D@?3@d/2-1.