On the global offensive alliance in unicycle graphs
For a graph , a set is a dominating set if every vertex in has at least a neighbor in . A dominating set is a global offensive alliance if for each vertex in at least half the vertices from the closed neighborhood of are in The domination number is the minimum cardinality of a dominating set of , an...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2018-04-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2018.01.001 |
| _version_ | 1818526325997043712 |
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| author | Mohamed Bouzefrane Saliha Ouatiki |
| author_facet | Mohamed Bouzefrane Saliha Ouatiki |
| author_sort | Mohamed Bouzefrane |
| collection | DOAJ |
| description | For a graph , a set is a dominating set if every vertex in has at least a neighbor in . A dominating set is a global offensive alliance if for each vertex in at least half the vertices from the closed neighborhood of are in The domination number is the minimum cardinality of a dominating set of , and the global offensive alliance number is the minimum cardinality of a global offensive alliance of . We show that if is a connected unicycle graph of order with leaves and support vertices then . Moreover, we characterize all extremal unicycle graphs attaining this bound. |
| first_indexed | 2024-12-11T06:21:22Z |
| format | Article |
| id | doaj.art-a8ec80c038084c4c8c64122a8c534f53 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 |
| language | English |
| last_indexed | 2024-12-11T06:21:22Z |
| publishDate | 2018-04-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-a8ec80c038084c4c8c64122a8c534f532022-12-22T01:17:48ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002018-04-01151727810.1016/j.akcej.2018.01.00112092638On the global offensive alliance in unicycle graphsMohamed Bouzefrane0Saliha Ouatiki1Department of Mathematics, B.P. 270, University of BlidaDepartment of Mathematics, University of BoumerdesFor a graph , a set is a dominating set if every vertex in has at least a neighbor in . A dominating set is a global offensive alliance if for each vertex in at least half the vertices from the closed neighborhood of are in The domination number is the minimum cardinality of a dominating set of , and the global offensive alliance number is the minimum cardinality of a global offensive alliance of . We show that if is a connected unicycle graph of order with leaves and support vertices then . Moreover, we characterize all extremal unicycle graphs attaining this bound.http://dx.doi.org/10.1016/j.akcej.2018.01.001dominationglobal offensive allianceunicycle graph |
| spellingShingle | Mohamed Bouzefrane Saliha Ouatiki On the global offensive alliance in unicycle graphs AKCE International Journal of Graphs and Combinatorics domination global offensive alliance unicycle graph |
| title | On the global offensive alliance in unicycle graphs |
| title_full | On the global offensive alliance in unicycle graphs |
| title_fullStr | On the global offensive alliance in unicycle graphs |
| title_full_unstemmed | On the global offensive alliance in unicycle graphs |
| title_short | On the global offensive alliance in unicycle graphs |
| title_sort | on the global offensive alliance in unicycle graphs |
| topic | domination global offensive alliance unicycle graph |
| url | http://dx.doi.org/10.1016/j.akcej.2018.01.001 |
| work_keys_str_mv | AT mohamedbouzefrane ontheglobaloffensiveallianceinunicyclegraphs AT salihaouatiki ontheglobaloffensiveallianceinunicyclegraphs |