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General Results

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

Abstract

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.

Keywords

Proper Connection Number Single Vertex Vertex Deletion Edge Deletion Internal Vertices 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    Andrews, E., Laforge, E., Lumduanhom, C., Zhang, P.: On proper-path colorings in graphs. J. Combin. Math. Combin. Comput. 97, 189–207 (2016)MathSciNetzbMATHGoogle Scholar
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    Andrews, E., Laforge, E., Lumduanhom, C., Zhang, P.: Proper-path colorings in graph operations. ManuscriptGoogle Scholar
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    Huang, F., Li, X., Wang, S.: Proper connection numbers of complementary graphs. Bull. Malays. Math. Sci. Soc. https://doi.org/10.1007/s40840-016-0381-8
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    Laforge, E., Lumduanhom, C., Zhang, P.: Characterizations of graphs having large proper connection numbers. Discuss. Math. Graph Theory 36(2), 439–454 (2016)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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