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A remark on degree sequences of multigraphs

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  • Dirk Meierling
  • Lutz Volkmann

Abstract

A sequence {d 1 , d 2 , . . . , d n } of nonnegative integers is graphic (multigraphic) if there exists a simple graph (multigraph) with vertices v 1 , v 2 , . . . , v n such that the degree d(v i ) of the vertex v i equals d i for each i = 1, 2, . . . , n. The (multi) graphic degree sequence problem is: Given a sequence of nonnegative integers, determine whether it is (multi)graphic or not. In this paper we characterize sequences that are multigraphic in a similar way, Havel (Časopis Pěst Mat 80:477–480, 1955) and Hakimi (J Soc Indust Appl Math 10:496–506, 1962) characterized graphic sequences. Results of Hakimi (J Soc Indust Appl Math 10:496–506, 1962) and Butler, Boesch and Harary (IEEE Trans Circuits Syst CAS-23(12):778–782, 1976) follow. Copyright Springer-Verlag 2009

Suggested Citation

  • Dirk Meierling & Lutz Volkmann, 2009. "A remark on degree sequences of multigraphs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(2), pages 369-374, May.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:2:p:369-374
    DOI: 10.1007/s00186-008-0265-2
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    Keywords

    Multigraph; Degree sequence;

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