The Connected Detour Numbers of Special Classes of Connected Graphs
Simple finite connected graphs G=V,E of p≥2 vertices are considered in this paper. A connected detour set of G is defined as a subset S⊆V such that the induced subgraph GS is connected and every vertex of G lies on a u−v detour for some u,v∈S. The connected detour number cdnG of a graph G is the min...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/8272483 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559281602297856 |
|---|---|
| author | Ahmed M. Ali Ali A. Ali |
| author_facet | Ahmed M. Ali Ali A. Ali |
| author_sort | Ahmed M. Ali |
| collection | DOAJ |
| description | Simple finite connected graphs G=V,E of p≥2 vertices are considered in this paper. A connected detour set of G is defined as a subset S⊆V such that the induced subgraph GS is connected and every vertex of G lies on a u−v detour for some u,v∈S. The connected detour number cdnG of a graph G is the minimum order of the connected detour sets of G. In this paper, we determined cdnG for three special classes of graphs G, namely, unicyclic graphs, bicyclic graphs, and cog-graphs for Cp, Kp, and Km,n. |
| format | Article |
| id | doaj-art-69681bee4add45d88a344acf6750a540 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-69681bee4add45d88a344acf6750a5402025-02-03T01:30:28ZengWileyJournal of Mathematics2314-46292314-47852019-01-01201910.1155/2019/82724838272483The Connected Detour Numbers of Special Classes of Connected GraphsAhmed M. Ali0Ali A. Ali1Department of Mathematics, College of Computer Science and Mathematics, Mosul University, Mosul, IraqDepartment of Mathematics, College of Computer Science and Mathematics, Mosul University, Mosul, IraqSimple finite connected graphs G=V,E of p≥2 vertices are considered in this paper. A connected detour set of G is defined as a subset S⊆V such that the induced subgraph GS is connected and every vertex of G lies on a u−v detour for some u,v∈S. The connected detour number cdnG of a graph G is the minimum order of the connected detour sets of G. In this paper, we determined cdnG for three special classes of graphs G, namely, unicyclic graphs, bicyclic graphs, and cog-graphs for Cp, Kp, and Km,n.http://dx.doi.org/10.1155/2019/8272483 |
| spellingShingle | Ahmed M. Ali Ali A. Ali The Connected Detour Numbers of Special Classes of Connected Graphs Journal of Mathematics |
| title | The Connected Detour Numbers of Special Classes of Connected Graphs |
| title_full | The Connected Detour Numbers of Special Classes of Connected Graphs |
| title_fullStr | The Connected Detour Numbers of Special Classes of Connected Graphs |
| title_full_unstemmed | The Connected Detour Numbers of Special Classes of Connected Graphs |
| title_short | The Connected Detour Numbers of Special Classes of Connected Graphs |
| title_sort | connected detour numbers of special classes of connected graphs |
| url | http://dx.doi.org/10.1155/2019/8272483 |
| work_keys_str_mv | AT ahmedmali theconnecteddetournumbersofspecialclassesofconnectedgraphs AT aliaali theconnecteddetournumbersofspecialclassesofconnectedgraphs AT ahmedmali connecteddetournumbersofspecialclassesofconnectedgraphs AT aliaali connecteddetournumbersofspecialclassesofconnectedgraphs |