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(Strong) Total proper connection of some digraphs

Author

Listed:
  • Yingbin Ma

    (Henan Normal University)

  • Kairui Nie

    (Henan Normal University)

Abstract

The total proper connection number of a given digraph D, represented by $$\overrightarrow{tpc}(D)$$ tpc → ( D ) , denotes the smallest number of colors needed for making D total proper connected. The strong total proper connection number of D, represented by $$\overrightarrow{stpc}(D)$$ stpc → ( D ) , shows the smallest number of colors required for making D strong total proper connected. In the present work, we represent some preliminary findings on $$\overrightarrow{tpc}(D)$$ tpc → ( D ) and $$\overrightarrow{stpc}(D)$$ stpc → ( D ) . Moreover, findings on the (strong) total proper connection numbers of biorientations of graphs, circle digraphs, circulant digraphs and cacti digraphs are provided.

Suggested Citation

  • Yingbin Ma & Kairui Nie, 2021. "(Strong) Total proper connection of some digraphs," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 24-39, July.
    • Handle: RePEc:spr:jcomop:v:42:y:2021:i:1:d:10.1007_s10878-021-00738-w
    DOI: 10.1007/s10878-021-00738-w
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    References listed on IDEAS

    as
    1. Hui Lei & Shasha Li & Henry Liu & Yongtang Shi, 2018. "Rainbow vertex connection of digraphs," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 86-107, January.
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