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Let G be a graph obtained from a graph G with no loops or coloops by replacing each edge e=uw of G by a connected graph H e that has only the vertices u and w in common with the rest of G. Two mutually dual formulas are proved for the Tutte polynomial of G in terms of parameters of the graphs H e and (in the one case) flow polynomials of subgraphs of G or (in the other case) tension...
Let P be the Petersen graph. The main results of this paper are the discovery of infinite families of chromatically equivalent pairs of P homeomorphs and the discovery of infinite families of flow equivalent pairs of P amallamorphs. In particular, three families of P homeomorphs with 8 parameters, five families with 7 parameters and many families with fewer parameters are obtained. Also one family...
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