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Full friendly index sets of mCn

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Abstract

Let G be a connected simple graph with vertex set V(G) and edge set E(G). A binary vertex labeling f: V(G) → ℤ2, is said to be friendly if the number of vertices with different labels differs by at most one. Each vertex friendly labeling f induces an edge labeling f*: E(G) → ℤ2, defined by f*(xy) = f(x) + f(y) for each xy ∈ E(G). Let ef*(i) = |{e ∈ E(G): f*(e) = i}|. The full friendly index set of G, denoted by FFI(G), is the set {ef*(1) − ef*(0): f is friendly}. In this paper, we determine the full friendly index set of a family of cycle union graphs which are edge subdivisions of P2 × Pn.

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References

  1. Gallian J A. A dynamic survey of graph labeling. Electronic Journal of Combinatorics, 2009, 19: 1–219

    Google Scholar 

  2. Cahit I. Cordial graphs: a weaker version of graceful and harmonious graphs. Ars Combinatoria, 1987, 23: 201–207

    MathSciNet  MATH  Google Scholar 

  3. Hovey M. A-cordial graphs. Discrete Mathematics, 1991, 93(2–3): 183–194

    Article  MathSciNet  MATH  Google Scholar 

  4. Chartrand G, Lee S M, Zhang P. Uniformly cordial graphs. Discrete Mathematics, 2006, 306(8–9): 726–737

    Article  MathSciNet  MATH  Google Scholar 

  5. Shiu W C, Kwong H. Full friendly index sets of P2×Pn. Discrete Mathematics, 2008, 308(16): 3688–3693

    Article  MathSciNet  MATH  Google Scholar 

  6. Hou J, Yan J. Max-Bisections of H-free graphs. Discrete Mathematics, 2020, 343(1): 111590

    Article  MathSciNet  MATH  Google Scholar 

  7. Liu Q, Dong X, Chen H, Wang Y. IncPregel: an incremental graph parallel computation model. Frontiers of Computer Science, 2018, 12(6): 1076–1089

    Article  Google Scholar 

  8. Wang Z, Chen Q, Suo B, Pan W, Li Z. Reducing partition skew on MapReduce: an incremental allocation approach. Frontiers of Computer Science, 2019, 13(5): 960–975

    Article  Google Scholar 

  9. Xu B. Graph partitions: recent progresses and some open problems. Advances in Mathematics (China), 2016, 45: 1–20

    MathSciNet  MATH  Google Scholar 

  10. Sinha D, Kaur J. Full friendly index set-I. Discrete Applied Mathematics, 2013, 161(9): 1262–1274

    Article  MathSciNet  MATH  Google Scholar 

  11. Shiu W C, Ling M H. Full friendly index sets of Cartesian products of two cycles. Acta Mathematica Sinica-English Series, 2010, 26(7): 1233–1244

    Article  MathSciNet  MATH  Google Scholar 

  12. Shiu W C, Wong F S. Full friendly index sets of cylinder graphs. Australasian Journal of Combinatorics, 2012, 52: 141–162

    MathSciNet  MATH  Google Scholar 

  13. Shiu W C, Ho M H. Full friendly index sets and full product-cordial index sets of some permutation Petersen graphs. Journal of Combinatorics and Number Theory, 2013, 5(3): 227–244

    MathSciNet  MATH  Google Scholar 

  14. Shiu W C, Ho M H. Full friendly index sets of slender and flat cylinder graphs. Transactions on Combinatorics, 2013, 2(4): 63–80

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We would like to thank the referees for providing some very helpful suggestions for revising this paper. This work was supported partly by the National Natural Science Foundation of China (Grant Nos. 11801149, 11801148). S. Wu was also partially supported by the Doctoral Fund of Henan Polytechnic University (B2018-55).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454003, China

    Yurong Ji, Yujie Bai & Shufei Wu

  2. Basic Department, Henan College of Industry and Information Technology, Jiaozuo, 454003, China

    Jinmeng Liu

Authors
  1. Yurong Ji
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  2. Jinmeng Liu
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  3. Yujie Bai
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  4. Shufei Wu
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Corresponding author

Correspondence to Shufei Wu.

Additional information

Yurong Ji is currently an associate professor in the School of Mathematics and Information Science at Henan Polytechnic University, China. Her research interests include graphical indices.

Jinmeng Liu received the Graduate degree from Henan Polytechnic University, China in 2015. She is currently a teaching assistant in the Basic Department at Henan College of Industry and Information Technology, China. Her research interests include graph theory (including graph drawing) in computer science.

Yujie Bai is now pursuing her master degree in the School of Mathematics and Information Science at Henan Polytechnic University, China. Her research interests include enumeration in graph theory.

Shufei Wu received the PhD degree from Fuzhou University, China in 2017. He is currently a lecture in the School of Mathematics and Information Science at Henan Polytechnic University, China. His research interests include probabilistic methods extremal combinatorics.

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Ji, Y., Liu, J., Bai, Y. et al. Full friendly index sets of mCn. Front. Comput. Sci. 16, 163403 (2022). https://doi.org/10.1007/s11704-021-0415-8

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  • DOI: https://doi.org/10.1007/s11704-021-0415-8

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