Abstract
ABSTRACTGiven a finite connected graph and a basis for a hyperplane in the cycle space of G, define summing over all connected spanning subgraphs Y of G such that with denoting the unique cycle in Y. We will show that is an element of the harmonic space where is the incidence matrix of G by establishing an inner product formula for the cycles z and the tree number k(G) of G. Several examples and applications of these formulas will be given.
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