Mathematics in Computer Science

, Volume 9, Issue 4, pp 437–441 | Cite as

Spiders can be Recognized by Counting Their Legs

  • Sarah J. Berkemer
  • Ricardo R. C. Chaves
  • Adrian Fritz
  • Marc HellmuthEmail author
  • Maribel Hernandez-Rosales
  • Peter F. Stadler


Spiders are arthropods that can be distinguished from their closest relatives, the insects, by counting their legs. Spiders have eight, insects just six. Spider graphs are a very restricted class of graphs that naturally appear in the context of cograph editing. The vertex set of a spider (or its complement) is naturally partitioned into a clique (the body), an independent set (the legs), and a rest (serving as the head). Here we show that spiders can be recognized directly from their degree sequences through the number of their legs (vertices with degree 1). Furthermore, we completely characterize the degree sequences of spiders.


Phylogenetics Cograph P4-sparse Spider Degree sequence 

Mathematics Subject Classification

Primary 05C07 Secondary 05C75 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Sarah J. Berkemer
    • 1
    • 2
  • Ricardo R. C. Chaves
    • 3
  • Adrian Fritz
    • 4
  • Marc Hellmuth
    • 4
    • 5
    Email author
  • Maribel Hernandez-Rosales
    • 3
    • 6
  • Peter F. Stadler
    • 1
    • 2
    • 7
    • 8
    • 9
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Bioinformatics Group, Department of Computer Science, Interdisciplinary Center for BioinformaticsUniversity of LeipzigLeipzigGermany
  3. 3.Departamento de Ciência da Computação (CIC), Instituto de Ciências ExatasUniversidade de BrasíliaBrasíliaBrazil
  4. 4.Center for BioinformaticsSaarland UniversitySaarbrückenGermany
  5. 5.Department of Mathematics and Computer ScienceUniversityof GreifswaldGreifswaldGermany
  6. 6.Instituto de MatemáticasUNAM JuriquillaSantiago de QuerétaroMexico
  7. 7.RNomics GroupFraunhofer Institut für Zelltherapie und ImmunologieLeipzigGermany
  8. 8.Department of Theoretical ChemistryUniversity of ViennaViennaAustria
  9. 9.Santa Fe InstituteSanta FeUSA

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