ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES
A subset \( H \subseteq V (G) \) of a graph \(G\) is a hop dominating set (HDS) if for every \({v\in (V\setminus H)}\) there is at least one vertex \(u\in H\) such that \(d(u,v)=2\). The minimum cardinality of a hop dominating set of \(G\) is called the hop domination number of \(G\) and is denote...
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2021-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/399 |
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| author | S. Shanmugavelan C. Natarajan |
| author_facet | S. Shanmugavelan C. Natarajan |
| author_sort | S. Shanmugavelan |
| collection | DOAJ |
| description | A subset \( H \subseteq V (G) \) of a graph \(G\) is a hop dominating set (HDS) if for every \({v\in (V\setminus H)}\) there is at least one vertex \(u\in H\) such that \(d(u,v)=2\). The minimum cardinality of a hop dominating set of \(G\) is called the hop domination number of \(G\) and is denoted by \(\gamma_{h}(G)\). In this paper, we compute the hop domination number for triangular and quadrilateral snakes. Also, we analyse the hop domination number of graph families such as generalized thorn path, generalized ciliates graphs, glued path graphs and generalized theta graphs. |
| format | Article |
| id | doaj-art-aa4ba76e4d9740feaed32c8e50cf79db |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2021-12-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-aa4ba76e4d9740feaed32c8e50cf79db2025-08-20T03:57:00ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522021-12-017210.15826/umj.2021.2.009135ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURESS. Shanmugavelan0C. Natarajan1Srinivasa Ramanujan Centre, SASTRA Deemed to be University, Kumbakonam–612001Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam-612001A subset \( H \subseteq V (G) \) of a graph \(G\) is a hop dominating set (HDS) if for every \({v\in (V\setminus H)}\) there is at least one vertex \(u\in H\) such that \(d(u,v)=2\). The minimum cardinality of a hop dominating set of \(G\) is called the hop domination number of \(G\) and is denoted by \(\gamma_{h}(G)\). In this paper, we compute the hop domination number for triangular and quadrilateral snakes. Also, we analyse the hop domination number of graph families such as generalized thorn path, generalized ciliates graphs, glued path graphs and generalized theta graphs.https://umjuran.ru/index.php/umj/article/view/399hop domination number, snake graphs, theta graphs, generalized thorn path |
| spellingShingle | S. Shanmugavelan C. Natarajan ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES Ural Mathematical Journal hop domination number, snake graphs, theta graphs, generalized thorn path |
| title | ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES |
| title_full | ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES |
| title_fullStr | ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES |
| title_full_unstemmed | ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES |
| title_short | ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES |
| title_sort | on hop domination number of some generalized graph structures |
| topic | hop domination number, snake graphs, theta graphs, generalized thorn path |
| url | https://umjuran.ru/index.php/umj/article/view/399 |
| work_keys_str_mv | AT sshanmugavelan onhopdominationnumberofsomegeneralizedgraphstructures AT cnatarajan onhopdominationnumberofsomegeneralizedgraphstructures |