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A graph is introduced, which allows of a combinatorial interpretation of a discrete-time semi-infinite Lotka-Volterra (dLV) equation. In particular, Hankel determinants used in a determinant solution to the dLV equation are evaluated, via the Gessel-Viennot method, in terms of non-intersecting subgraphs. Further, the recurrence of the dLV equation describing its time-evolution is equivalently expressed as a time-evolution of weight of specific subgraphs.