Graphs and Combinatorics

, Volume 5, Issue 1, pp 283–290 | Cite as

Implicit-degrees and circumferences

  • Zhu Yongjin
  • Li Hao
  • Deng Xiaotie


In this paper, we introduce a new concept — implicit-degrees of vertices of graphs. Related to this concept, a new definition for the closure of a graph is introduced. This closure is obtained by recursively joining pairs of nonadjacent vertices whose implicit-degree sum is at least the order of the graph. A criterion for deciding whether a graph is hamiltonian from its closure is obtained. Two other important results concerning the implicit-degrees of vertices and circumferences of graphs are presented.


Nonadjacent Vertex 
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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Zhu Yongjin
    • 1
  • Li Hao
    • 1
  • Deng Xiaotie
    • 1
  1. 1.Institute of Systems ScienceAcademia SinicaBeijingPeople's Republic of China

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