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Enumerating simple paths from connected induced subgraphs (1606.00289v2)
Published 1 Jun 2016 in math.CO
Abstract: We present an exact formula for the ordinary generating series of the simple paths between any two vertices of a graph. Our formula involves the adjacency matrix of the connected induced subgraphs and remains valid on weighted and directed graphs. As a particular case, we obtain a relation linking the Hamiltonian paths and cycles of a graph to its dominating connected sets.
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