For a nonregular graph there is exactly one value of p such that the p-mean of its degree sequence is equal to the spectral radius. We try to investigate the structural content of this so-called spectral mean characteristic; in particular, me characterize the connected graphs of spectral mean characteristic 2.
Any group of automorphisms of a graph G induces a notion of isomorphism between double covers of G. The corresponding isomorphism classes will be counted.
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