(Strong) Total proper connection of some digraphs

Yingbin Ma () and Kairui Nie ()
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Yingbin Ma: Henan Normal University
Kairui Nie: Henan Normal University

Journal of Combinatorial Optimization, 2021, vol. 42, issue 1, No 2, 24-39

Abstract: 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.

Keywords: Total proper path; Total proper geodesic; tpc-number; stpc-number; 05C15; 05C35; 05C40 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10878-021-00738-w

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