The 2-distance vertex distinguishing index  of a graph G is the minimum number of colors needed for a proper edge coloring such that for any pair of vertices at distance two, the sets of colors on their incident edges are distinct. In this paper, we prove that every graph G with maximum degree  and maximum average degree less than  has

sparse graphs, 2-distance vertex distinguishing edge coloring, discharging method.

Received: June 20, 2022; Accepted: July 16, 2022; Published: July 25, 2022

How to cite this article: Lomngam Kamga Victor and Ebodé Atangana Pie Désire, 2-distance vertex distinguishing index of sparse graphs, Advances and Applications in Discrete Mathematics 33 (2022), 1-18. http://dx.doi.org/10.17654/0974165822035

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] A. Bondy and U. Murty, Graph theory, Graduate Texts in Mathematics, Springer, London, 2011.
[2] D. Huang, K.-W. Lih and W. Wang, Legally (D + 2) -coloring bipartite outerplanar graphs in cubic time, Combinatorial Optimization and Applications, Lecture Notes in Comput. Sci., 2015, pp. 617-632.
[3] D. Huang, Y. Wang, W. Wang and Y. Wang, 2-distance vertex-distinguishing edge colorings of graphs, International Journal of Mathematics and Statistics 21(3) (2020), 1-19.
[4] V. K. Loumngam, J. Liu and W. Wang, Two-distance vertex-distinguishing index of sparse subcubic graphs, Bull. Malays. Math. Sci. Soc. 43 (2020), 3183-3199.
[5] V. K. Loumngam, W. Wang, Y. Wang and M. Chen, 2-distance vertexdistinguishing index of subcubic graphs, J. Comb. Optim. 36(1) (2018), 108-120.
[6] J. Przybyło, Distant set distinguishing edge colourings of graphs, European J. Combin. 69 (2018), 185-199.
[7] Z. Zhang, L. Liu and J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett. 15 (2002), 623-626.