Double total domination number in certain chemical graphs
Let $ G $ be a graph with the vertex set $ V(G) $. A set $ D\subseteq V(G) $ is a total k-dominating set if every vertex $ v\in V(G) $ has at least $ k $ neighbours in $ D $. The total k-domination number $ \gamma_{kt}(G) $ is the cardinality of the smallest total k-dominating set. For $ k = 2 $ the...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20221076?viewType=HTML |
| _version_ | 1818049559707779072 |
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| author | Ana Klobučar Barišić Antoaneta Klobučar |
| author_facet | Ana Klobučar Barišić Antoaneta Klobučar |
| author_sort | Ana Klobučar Barišić |
| collection | DOAJ |
| description | Let $ G $ be a graph with the vertex set $ V(G) $. A set $ D\subseteq V(G) $ is a total k-dominating set if every vertex $ v\in V(G) $ has at least $ k $ neighbours in $ D $. The total k-domination number $ \gamma_{kt}(G) $ is the cardinality of the smallest total k-dominating set. For $ k = 2 $ the total 2-dominating set is called double total dominating set. In this paper we determine the upper and lower bounds and some exact values for double total domination number on pyrene network $ PY(n) $, $ n\geq 1 $ and hexabenzocoronene $ XC(n) $ $ n\geq 2 $, where pyrene network and hexabenzocoronene are composed of congruent hexagons. |
| first_indexed | 2024-12-10T10:39:31Z |
| format | Article |
| id | doaj.art-34377a3ace22422aba25158957651085 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-10T10:39:31Z |
| publishDate | 2022-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-34377a3ace22422aba251589576510852022-12-22T01:52:21ZengAIMS PressAIMS Mathematics2473-69882022-09-01711196291964010.3934/math.20221076Double total domination number in certain chemical graphsAna Klobučar Barišić0Antoaneta Klobučar11. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia2. Faculty of Economics, Josip Juraj Strossmayer University of Osijek, Osijek, CroatiaLet $ G $ be a graph with the vertex set $ V(G) $. A set $ D\subseteq V(G) $ is a total k-dominating set if every vertex $ v\in V(G) $ has at least $ k $ neighbours in $ D $. The total k-domination number $ \gamma_{kt}(G) $ is the cardinality of the smallest total k-dominating set. For $ k = 2 $ the total 2-dominating set is called double total dominating set. In this paper we determine the upper and lower bounds and some exact values for double total domination number on pyrene network $ PY(n) $, $ n\geq 1 $ and hexabenzocoronene $ XC(n) $ $ n\geq 2 $, where pyrene network and hexabenzocoronene are composed of congruent hexagons.https://www.aimspress.com/article/doi/10.3934/math.20221076?viewType=HTMLtotal dominationdouble total dominationhexagonal systemsmolecular graphpyrene networkhexabenzocoronene |
| spellingShingle | Ana Klobučar Barišić Antoaneta Klobučar Double total domination number in certain chemical graphs AIMS Mathematics total domination double total domination hexagonal systems molecular graph pyrene network hexabenzocoronene |
| title | Double total domination number in certain chemical graphs |
| title_full | Double total domination number in certain chemical graphs |
| title_fullStr | Double total domination number in certain chemical graphs |
| title_full_unstemmed | Double total domination number in certain chemical graphs |
| title_short | Double total domination number in certain chemical graphs |
| title_sort | double total domination number in certain chemical graphs |
| topic | total domination double total domination hexagonal systems molecular graph pyrene network hexabenzocoronene |
| url | https://www.aimspress.com/article/doi/10.3934/math.20221076?viewType=HTML |
| work_keys_str_mv | AT anaklobucarbarisic doubletotaldominationnumberincertainchemicalgraphs AT antoanetaklobucar doubletotaldominationnumberincertainchemicalgraphs |