(Strong) Proper Connection in Some Digraphs
An arc-colored digraph D is proper connected if any pair of vertices vi, vj ε V(D) there is a proper vi - vj path whose adjacent arcs have different colors and a proper vj - vi path whose adjacent arcs have different colors. The proper connection number of a digraph D is the minimum numbe...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8720152/ |
| _version_ | 1818323873430503424 |
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| author | Yingbin Ma Kairui Nie |
| author_facet | Yingbin Ma Kairui Nie |
| author_sort | Yingbin Ma |
| collection | DOAJ |
| description | An arc-colored digraph D is proper connected if any pair of vertices vi, vj ε V(D) there is a proper vi - vj path whose adjacent arcs have different colors and a proper vj - vi path whose adjacent arcs have different colors. The proper connection number of a digraph D is the minimum number of colors needed to make D proper connected, denoted by spc(D). An arc-colored digraph D is strong proper connected if any pair of vertices vi, vj ε V(D) there is a proper vi - vj geodesic and a proper vj - vi geodesic. The strong proper connection number of D is the minimum number of colors required to color the arcs of D in order to make D strong proper connected, denoted by spc(D). In this paper, we will show some results on spc(D) and spc(D), mostly for the case of the (strong) proper connection numbers of cacti and circulant digraphs. |
| first_indexed | 2024-12-13T11:19:36Z |
| format | Article |
| id | doaj.art-424fb45961834388b562e67f36814444 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-13T11:19:36Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-424fb45961834388b562e67f368144442022-12-21T23:48:31ZengIEEEIEEE Access2169-35362019-01-017696926969710.1109/ACCESS.2019.29183688720152(Strong) Proper Connection in Some DigraphsYingbin Ma0https://orcid.org/0000-0002-9875-3136Kairui Nie1College of Mathematics and Information Science, Henan Normal University, Xinxiang, ChinaCollege of Mathematics and Information Science, Henan Normal University, Xinxiang, ChinaAn arc-colored digraph D is proper connected if any pair of vertices vi, vj ε V(D) there is a proper vi - vj path whose adjacent arcs have different colors and a proper vj - vi path whose adjacent arcs have different colors. The proper connection number of a digraph D is the minimum number of colors needed to make D proper connected, denoted by spc(D). An arc-colored digraph D is strong proper connected if any pair of vertices vi, vj ε V(D) there is a proper vi - vj geodesic and a proper vj - vi geodesic. The strong proper connection number of D is the minimum number of colors required to color the arcs of D in order to make D strong proper connected, denoted by spc(D). In this paper, we will show some results on spc(D) and spc(D), mostly for the case of the (strong) proper connection numbers of cacti and circulant digraphs.https://ieeexplore.ieee.org/document/8720152/Proper pathproper connection numberproper geodesicstrong proper connection number |
| spellingShingle | Yingbin Ma Kairui Nie (Strong) Proper Connection in Some Digraphs IEEE Access Proper path proper connection number proper geodesic strong proper connection number |
| title | (Strong) Proper Connection in Some Digraphs |
| title_full | (Strong) Proper Connection in Some Digraphs |
| title_fullStr | (Strong) Proper Connection in Some Digraphs |
| title_full_unstemmed | (Strong) Proper Connection in Some Digraphs |
| title_short | (Strong) Proper Connection in Some Digraphs |
| title_sort | strong proper connection in some digraphs |
| topic | Proper path proper connection number proper geodesic strong proper connection number |
| url | https://ieeexplore.ieee.org/document/8720152/ |
| work_keys_str_mv | AT yingbinma strongproperconnectioninsomedigraphs AT kairuinie strongproperconnectioninsomedigraphs |