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Dominated coloring in product graphs

Author

Listed:
  • Minhui Li

    (Qinghai Normal University)

  • Shumin Zhang

    (Qinghai Normal University
    People’s Government of Qinghai Province and Beijing Normal University)

  • Chengfu Ye

    (Qinghai Normal University
    People’s Government of Qinghai Province and Beijing Normal University)

Abstract

The dominated coloring (dom-coloring) of a graph G is a proper coloring such that each color class is dominated by at least one vertex. The dominated chromatic number (dom-chromatic number) of G is the minimum number of color classes among all dominated colorings of G, denoted by $$\chi _{\text {dom}}(G)$$ χ dom ( G ) . In this paper, we study the dominated coloring of Cartesian product, direct product, lexicographic product and strong product of some graphs.

Suggested Citation

  • Minhui Li & Shumin Zhang & Chengfu Ye, 2023. "Dominated coloring in product graphs," Journal of Combinatorial Optimization, Springer, vol. 46(4), pages 1-11, November.
    • Handle: RePEc:spr:jcomop:v:46:y:2023:i:4:d:10.1007_s10878-023-01094-7
    DOI: 10.1007/s10878-023-01094-7
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