A Collection of Minimally Path Square-Saturated Graphs
Given a simple graph G, m a positive integer. The square of path graph P_m, denoted by P_m^2, is a graph obtained from P_m by adding new edges between any pair of vertices at distance at most 2 in P_m. A graph G is P_m^2-saturated if G does not contain P_m^2 as a subgraph, but the addition of any ed...
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| Format: | Article |
| Language: | English |
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UIN Sunan Gunung Djati Bandung, Mathematics Department
2020-10-01
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| Series: | Kubik |
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| Online Access: | https://journal.uinsgd.ac.id/index.php/kubik/article/view/8415 |
| _version_ | 1828081911212277760 |
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| author | Salwa Nursyahida |
| author_facet | Salwa Nursyahida |
| author_sort | Salwa Nursyahida |
| collection | DOAJ |
| description | Given a simple graph G, m a positive integer. The square of path graph P_m, denoted by P_m^2, is a graph obtained from P_m by adding new edges between any pair of vertices at distance at most 2 in P_m. A graph G is P_m^2-saturated if G does not contain P_m^2 as a subgraph, but the addition of any edge between two nonadjacent vertices in G contain P_m^2. The minimum size of P_m^2-saturated graph on n vertices is called a saturation number for P_m^2, denoted by sat(n,P_m^2). A set Sat(n,P_m^2 )={G:|V(G)|=sat(n,P_m^2) and G a P_m^2-saturated graph}. All graphs in Sat(n,P_m^2) are obtained computationally for n≤8 and m≤8 and expressed by their degree sequence. |
| first_indexed | 2024-04-11T03:43:21Z |
| format | Article |
| id | doaj.art-85b672f41adf40cc8244618f7e5e3854 |
| institution | Directory Open Access Journal |
| issn | 2338-0896 2686-0341 |
| language | English |
| last_indexed | 2024-04-11T03:43:21Z |
| publishDate | 2020-10-01 |
| publisher | UIN Sunan Gunung Djati Bandung, Mathematics Department |
| record_format | Article |
| series | Kubik |
| spelling | doaj.art-85b672f41adf40cc8244618f7e5e38542023-01-02T03:25:39ZengUIN Sunan Gunung Djati Bandung, Mathematics DepartmentKubik2338-08962686-03412020-10-0151202710.15575/kubik.v5i1.84154051A Collection of Minimally Path Square-Saturated GraphsSalwa Nursyahida0UIN Sunan Gunung Djati BandungGiven a simple graph G, m a positive integer. The square of path graph P_m, denoted by P_m^2, is a graph obtained from P_m by adding new edges between any pair of vertices at distance at most 2 in P_m. A graph G is P_m^2-saturated if G does not contain P_m^2 as a subgraph, but the addition of any edge between two nonadjacent vertices in G contain P_m^2. The minimum size of P_m^2-saturated graph on n vertices is called a saturation number for P_m^2, denoted by sat(n,P_m^2). A set Sat(n,P_m^2 )={G:|V(G)|=sat(n,P_m^2) and G a P_m^2-saturated graph}. All graphs in Sat(n,P_m^2) are obtained computationally for n≤8 and m≤8 and expressed by their degree sequence.https://journal.uinsgd.ac.id/index.php/kubik/article/view/8415power graphs, path square, saturated numbers, saturated graphs, degree sequence of graph |
| spellingShingle | Salwa Nursyahida A Collection of Minimally Path Square-Saturated Graphs Kubik power graphs, path square, saturated numbers, saturated graphs, degree sequence of graph |
| title | A Collection of Minimally Path Square-Saturated Graphs |
| title_full | A Collection of Minimally Path Square-Saturated Graphs |
| title_fullStr | A Collection of Minimally Path Square-Saturated Graphs |
| title_full_unstemmed | A Collection of Minimally Path Square-Saturated Graphs |
| title_short | A Collection of Minimally Path Square-Saturated Graphs |
| title_sort | collection of minimally path square saturated graphs |
| topic | power graphs, path square, saturated numbers, saturated graphs, degree sequence of graph |
| url | https://journal.uinsgd.ac.id/index.php/kubik/article/view/8415 |
| work_keys_str_mv | AT salwanursyahida acollectionofminimallypathsquaresaturatedgraphs AT salwanursyahida collectionofminimallypathsquaresaturatedgraphs |