Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake Graph
Let G = (V(G), E(G)) be a connected graph, where V(G) is the set of vertices and E(G) is the set of edges. The set Dt(G) is called the total domination set in G if every vertex v 2 V(G) is adjacent to at least one vertex in Dt (G). Furthermore, Dt(G) must satisfy the property N(Dt ) = V(G), where N(...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Department of Mathematics, Universitas Negeri Gorontalo
2022-06-01
|
| Series: | Jambura Journal of Mathematics |
| Subjects: | |
| Online Access: | https://ejurnal.ung.ac.id/index.php/jjom/article/view/14176 |
| _version_ | 1828335538111774720 |
|---|---|
| author | Nurhamzah Nurhamzah Nilamsari Kusumastuti Fransiskus Fran |
| author_facet | Nurhamzah Nurhamzah Nilamsari Kusumastuti Fransiskus Fran |
| author_sort | Nurhamzah Nurhamzah |
| collection | DOAJ |
| description | Let G = (V(G), E(G)) be a connected graph, where V(G) is the set of vertices and E(G) is the set of edges. The set Dt(G) is called the total domination set in G if every vertex v 2 V(G) is adjacent to at least one vertex in Dt (G). Furthermore, Dt(G) must satisfy the property N(Dt ) = V(G), where N(Dt) is an open neighbourhood set of Dt(G). Suppose that Dt(G) is the total domination set with minimum cardinality. If V(G) - Dt(G) contains a total domination set Dt-1(G), then Dt-1(G) is the inverse set of total domination relative to the total domination set Dt (G). The inverse’s number of the total domination set denotes the minimum cardinality of the inverse set of total domination. This number is denoted by gt-1 (G). This article discusses the inverse’s number of total domination of the triangular snake graph (Tn), line triangular snake graph (L (Tn)), and shadow triangular snake graph (D2 (Tn)). Graph Tn is a graph obtained from the path graph (Pn) by replacing each side of the path with a cycle graph (C3). Graph L (Tn) is a graph where the vertex set in L(Tn) is the edge set on Tn, or V(L(Tn)) = E(Tn). Graph D2 (Tn) is a graph obtained by combining two copies of a graph Tn, namely Tn0 and T00n. This research shows that the graph Tn does not have an inverse of domination total, gt-1 (L (Tn)) = n for n = 4, 6, 8, gt-1 (L (Tn)) = n - 1 for n = 3, 5, 7, or n ≥ 9 with n 2 N, and gt-1 (D2 (Tn)) = b23nc for n ≥ 3 with n 2 N. |
| first_indexed | 2024-04-13T21:48:36Z |
| format | Article |
| id | doaj.art-fa4c68ba6b3b4aefb2185ffaacce7b47 |
| institution | Directory Open Access Journal |
| issn | 2654-5616 2656-1344 |
| language | English |
| last_indexed | 2024-04-13T21:48:36Z |
| publishDate | 2022-06-01 |
| publisher | Department of Mathematics, Universitas Negeri Gorontalo |
| record_format | Article |
| series | Jambura Journal of Mathematics |
| spelling | doaj.art-fa4c68ba6b3b4aefb2185ffaacce7b472022-12-22T02:28:29ZengDepartment of Mathematics, Universitas Negeri GorontaloJambura Journal of Mathematics2654-56162656-13442022-06-014210.34312/jjom.v4i2.141764229Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake GraphNurhamzah Nurhamzah0Nilamsari Kusumastuti1Fransiskus Fran2Jurusan Matematika, Fakultas MIPA, Universitas Tanjungpura, Jl. Prof. Dr. Hadari Nawawi, Kota Pontianak 78124, Kalimantan BaratJurusan Matematika, Fakultas MIPA, Universitas Tanjungpura, Jl. Prof. Dr. Hadari Nawawi, Kota Pontianak 78124, Kalimantan BaratJurusan Matematika, Fakultas MIPA, Universitas Tanjungpura, Jl. Prof. Dr. Hadari Nawawi, Kota Pontianak 78124, Kalimantan BaratLet G = (V(G), E(G)) be a connected graph, where V(G) is the set of vertices and E(G) is the set of edges. The set Dt(G) is called the total domination set in G if every vertex v 2 V(G) is adjacent to at least one vertex in Dt (G). Furthermore, Dt(G) must satisfy the property N(Dt ) = V(G), where N(Dt) is an open neighbourhood set of Dt(G). Suppose that Dt(G) is the total domination set with minimum cardinality. If V(G) - Dt(G) contains a total domination set Dt-1(G), then Dt-1(G) is the inverse set of total domination relative to the total domination set Dt (G). The inverse’s number of the total domination set denotes the minimum cardinality of the inverse set of total domination. This number is denoted by gt-1 (G). This article discusses the inverse’s number of total domination of the triangular snake graph (Tn), line triangular snake graph (L (Tn)), and shadow triangular snake graph (D2 (Tn)). Graph Tn is a graph obtained from the path graph (Pn) by replacing each side of the path with a cycle graph (C3). Graph L (Tn) is a graph where the vertex set in L(Tn) is the edge set on Tn, or V(L(Tn)) = E(Tn). Graph D2 (Tn) is a graph obtained by combining two copies of a graph Tn, namely Tn0 and T00n. This research shows that the graph Tn does not have an inverse of domination total, gt-1 (L (Tn)) = n for n = 4, 6, 8, gt-1 (L (Tn)) = n - 1 for n = 3, 5, 7, or n ≥ 9 with n 2 N, and gt-1 (D2 (Tn)) = b23nc for n ≥ 3 with n 2 N.https://ejurnal.ung.ac.id/index.php/jjom/article/view/14176total domination numberinverse total dominationopen neighborhood |
| spellingShingle | Nurhamzah Nurhamzah Nilamsari Kusumastuti Fransiskus Fran Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake Graph Jambura Journal of Mathematics total domination number inverse total domination open neighborhood |
| title | Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake Graph |
| title_full | Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake Graph |
| title_fullStr | Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake Graph |
| title_full_unstemmed | Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake Graph |
| title_short | Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake Graph |
| title_sort | bilangan invers dominasi total pada triangular snake graph line triangular snake graph dan shadow triangular snake graph |
| topic | total domination number inverse total domination open neighborhood |
| url | https://ejurnal.ung.ac.id/index.php/jjom/article/view/14176 |
| work_keys_str_mv | AT nurhamzahnurhamzah bilanganinversdominasitotalpadatriangularsnakegraphlinetriangularsnakegraphdanshadowtriangularsnakegraph AT nilamsarikusumastuti bilanganinversdominasitotalpadatriangularsnakegraphlinetriangularsnakegraphdanshadowtriangularsnakegraph AT fransiskusfran bilanganinversdominasitotalpadatriangularsnakegraphlinetriangularsnakegraphdanshadowtriangularsnakegraph |