Characterization of unigraphic and unidigraphic integer-pair sequences

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Abstract

Given a graph (digraph) G with edge (arc) set E(G) = {(u1}, υ1), (u2, υ2),⋯,(uq, υq, where q = |E(G)|, we can associate with it an integer-pair sequence SG = ((a1, b1), (a2, b2),⋯, (aq, bq)) where ai, bi are the degrees (indegrees) of ui, υi respectively. An integer- pair sequence S is said to be graphic (digraphic) if there exists a graph (digraph) G such that SG = S. In this paper we characterize unigraphic and unidigraphic integer-pair sequences.

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