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math.CO2001
A Heawood-type result for the algebraic connectivity of graphs on surfaces
Pedro Freitas
We prove that the algebraic connectivity a(G) of a graph embedded on a nonplanar surface satisfies a Heawood-type result. More precisely, it is shown that the algebraic connectivit…
math.AP2001
Characterization of harmonic and subharmonic functions via mean-value properties
Pedro Freitas, Joao Palhoto Matos
We give a characterization of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. This includes the converse of an inequality of Beardon's for…