Computing the l,k-Clique Metric Dimension of Graphs via (Edge) Corona Products and Integer Linear Programming Model
Let G be a graph with n vertices and CG=X:X is an l-clique of G. A vertex v∈VG is said to resolve a pair of cliques X,Y in G if dGv,X≠dGv,Y where dG is the distance function of G. For a pair of cliques X,Y, the resolving neighbourhood of X and Y, denoted by RGX,Y, is the collection of all vertices w...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/3241718 |
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| author | Zeinab Shahmiri Mostafa Tavakoli |
| author_facet | Zeinab Shahmiri Mostafa Tavakoli |
| author_sort | Zeinab Shahmiri |
| collection | DOAJ |
| description | Let G be a graph with n vertices and CG=X:X is an l-clique of G. A vertex v∈VG is said to resolve a pair of cliques X,Y in G if dGv,X≠dGv,Y where dG is the distance function of G. For a pair of cliques X,Y, the resolving neighbourhood of X and Y, denoted by RGX,Y, is the collection of all vertices which resolve the pair X,Y. A subset S of VG is called an l,k-clique metric generator for G if RGX,Y∩S≥k for each pair of distinct l-cliques X and Y of G. The l,k-clique metric dimension of G, denoted by l−cdimkG, is defined as minS:S is an l,k-clique metric generator of G. In this paper, the l,k-clique metric dimension of corona and edge corona of two graphs are computed. In addition, an integer linear programming model is presented for the l,k-clique metric basis for a given graph G and its l-cliques. |
| format | Article |
| id | doaj-art-c77287a4f1174767a1f0ed10a1191377 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c77287a4f1174767a1f0ed10a11913772025-02-03T05:56:54ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/3241718Computing the l,k-Clique Metric Dimension of Graphs via (Edge) Corona Products and Integer Linear Programming ModelZeinab Shahmiri0Mostafa Tavakoli1Department of Applied MathematicsDepartment of Applied MathematicsLet G be a graph with n vertices and CG=X:X is an l-clique of G. A vertex v∈VG is said to resolve a pair of cliques X,Y in G if dGv,X≠dGv,Y where dG is the distance function of G. For a pair of cliques X,Y, the resolving neighbourhood of X and Y, denoted by RGX,Y, is the collection of all vertices which resolve the pair X,Y. A subset S of VG is called an l,k-clique metric generator for G if RGX,Y∩S≥k for each pair of distinct l-cliques X and Y of G. The l,k-clique metric dimension of G, denoted by l−cdimkG, is defined as minS:S is an l,k-clique metric generator of G. In this paper, the l,k-clique metric dimension of corona and edge corona of two graphs are computed. In addition, an integer linear programming model is presented for the l,k-clique metric basis for a given graph G and its l-cliques.http://dx.doi.org/10.1155/2024/3241718 |
| spellingShingle | Zeinab Shahmiri Mostafa Tavakoli Computing the l,k-Clique Metric Dimension of Graphs via (Edge) Corona Products and Integer Linear Programming Model Journal of Mathematics |
| title | Computing the l,k-Clique Metric Dimension of Graphs via (Edge) Corona Products and Integer Linear Programming Model |
| title_full | Computing the l,k-Clique Metric Dimension of Graphs via (Edge) Corona Products and Integer Linear Programming Model |
| title_fullStr | Computing the l,k-Clique Metric Dimension of Graphs via (Edge) Corona Products and Integer Linear Programming Model |
| title_full_unstemmed | Computing the l,k-Clique Metric Dimension of Graphs via (Edge) Corona Products and Integer Linear Programming Model |
| title_short | Computing the l,k-Clique Metric Dimension of Graphs via (Edge) Corona Products and Integer Linear Programming Model |
| title_sort | computing the l k clique metric dimension of graphs via edge corona products and integer linear programming model |
| url | http://dx.doi.org/10.1155/2024/3241718 |
| work_keys_str_mv | AT zeinabshahmiri computingthelkcliquemetricdimensionofgraphsviaedgecoronaproductsandintegerlinearprogrammingmodel AT mostafatavakoli computingthelkcliquemetricdimensionofgraphsviaedgecoronaproductsandintegerlinearprogrammingmodel |