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On N2-vertex coloring of graphs

Akbari, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1142/S1793830918500076
  3. Abstract:
  4. Let (Formula presented.) be a graph. A vertex coloring (Formula presented.) of (Formula presented.) is called (Formula presented.)-vertex coloring if (Formula presented.) for every vertex (Formula presented.) of (Formula presented.), where (Formula presented.) is the set of colors of vertices adjacent to (Formula presented.). Let (Formula presented.) be the maximum number of colors used in an (Formula presented.)-vertex coloring of (Formula presented.). We provide some lower and upper bounds for (Formula presented.) in terms of girth, diameter or size of (Formula presented.). Also, for every tree (Formula presented.), we obtain (Formula presented.). © 2018 World Scientific Publishing Company
  5. Keywords:
  6. N2-vertex coloring ; Graph coloring
  7. Source: Discrete Mathematics, Algorithms and Applications ; 2017 ; 17938309 (ISSN)
  8. URL: https://www.worldscientific.com/doi/abs/10.1142/S1793830918500076