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(Strong) Total proper connection of some digraphs
Journal of Combinatorial Optimization ( IF 0.9 ) Pub Date : 2021-04-16 , DOI: 10.1007/s10878-021-00738-w
Yingbin Ma , Kairui Nie

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



中文翻译:

(强)某些有向图的完全正确连接

给定的有向图D的总正确连接数由\(\ overrightarrow {tpc}(D)\)表示,表示使D完全正确连接所需的最小颜色数。的强总正确的连接数d,表示为\(\ overrightarrow {STPC}(d)\),示出了用于制造所需要的颜色的最小数目d强总正确连接。在当前的工作中,我们代表了\(\ overrightarrow {tpc}(D)\)\(\ overrightarrow {stpc}(D)\)的一些初步发现。。此外,提供了关于图,圆有向图,循环有向图和仙人掌有向图的生物取向的(强)总适当连接数的发现。

更新日期:2021-04-16
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