Operations on Graphs

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


Among the many interesting problems of determining the proper connection numbers of graphs, it is worthwhile to study the proper connection number of G according to some constraints of the complementary graph.


  1. 1.
    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
  2. 2.
    Andrews, E., Laforge, E., Lumduanhom, C., Zhang, P.: Proper-path colorings in graph operations. ManuscriptGoogle Scholar
  3. 3.
    Aouchiche, M., Hansen, P.: A survey of Nordhaus-Gaddum type relations. Discrete Appl. Math. 161(4–5), 466–546 (2013)MathSciNetCrossRefGoogle Scholar
  4. 10.
    Bondy, J.A., Murty, U.S.R.: Graph Theory. Graduate Texts in Mathematics, vol. 244. Springer, New York (2008)CrossRefGoogle Scholar
  5. 35.
    Hammack, R.H., Taylor, D.T.: Proper connection of direct products. Discuss. Math. Graph Theory 37, 1005–1013 (2017)MathSciNetCrossRefGoogle Scholar
  6. 40.
    Huang, F., Li, X., Wang, S.: Proper connection numbers of complementary graphs. Bull. Malays. Math. Sci. Soc.
  7. 48.
    Laforge, E., Lumduanhom, C., Zhang, P.: Chromatic-connection in graphs. Congressus Numerantium (to appear)Google Scholar
  8. 60.
    Mao, Y., Yanling, F., Wang, Z., Ye, C.: Proper connection number of graph products. Bull. Malays. Math. Sci. Soc.

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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