General Results

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


In this chapter, we state some general results for proper connection number of graphs. There is an easy lower bound on pc(G) using the maximum number of bridges (cut edges) incident to a single vertex. All such bridges must receive distinct colors for the coloring to be proper connected, so the following result comes at no surprise.


Proper Connection Number Single Vertex Vertex Deletion Edge Deletion Internal Vertices 
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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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