Domination Conditions

  • Xueliang Li
  • Colton Magnant
  • Zhongmei Qin
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


Relating the proper connection number with domination, the following results were proven in Li et al. (Theor Comput Sci 607:480–487, 2015). A dominating set for a graph G = (V, E) is a subset D of V such that every vertex not in D is adjacent to at least one member of D. A dominating set D is called two-way two-step dominating if every pendant vertex is included in D and every vertex at distance at least 2 from D has at least two neighbors at distance 1 from D.


  1. 58.
    Li, X., Wei, M., Yue, J.: Proper connection number and connected dominating sets. Theor. Comput. Sci. 607, 480–487 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Xueliang Li
    • 1
  • Colton Magnant
    • 2
  • Zhongmei Qin
    • 3
  1. 1.Center for CombinatoricsNankai UniversityTianjinChina
  2. 2.Department of MathematicsGeorgia Southern UniversityStatesboroUSA
  3. 3.College of ScienceChang’an UniversityXi’anChina

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