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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |