Computing Bounds of Fractional Metric Dimension of Metal Organic Graphs
Metal organic graphs are hollow structures of metal atoms that are connected by ligands, where metal atoms are represented by the vertices and ligands are referred as edges. A vertex x resolves the vertices u and v of a graph G if du,x≠dv,x. For a pair u,v of vertices of G, Ru,v=x∈VG:dx,u≠dx,v is ca...
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Wiley
2021-01-01
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| Series: | Journal of Chemistry |
| Online Access: | http://dx.doi.org/10.1155/2021/5539569 |
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| author | Mohsin Raza Dalal Awadh Alrowaili Muhammad Javaid Khurram Shabbir |
| author_facet | Mohsin Raza Dalal Awadh Alrowaili Muhammad Javaid Khurram Shabbir |
| author_sort | Mohsin Raza |
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| description | Metal organic graphs are hollow structures of metal atoms that are connected by ligands, where metal atoms are represented by the vertices and ligands are referred as edges. A vertex x resolves the vertices u and v of a graph G if du,x≠dv,x. For a pair u,v of vertices of G, Ru,v=x∈VG:dx,u≠dx,v is called its resolving neighbourhood set. For each pair of vertices u and v in VG, if fRu,v≥1, then f from VG to the interval 0,1 is called resolving function. Moreover, for two functions f and g, f is called minimal if f≤g and fv≠gv for at least one v∈VG. The fractional metric dimension (FMD) of G is denoted by dimfG and defined as dimfG=ming:g is a minimal resolving function of G, where g=∑v∈VGgv. If we take a pair of vertices u,v of G as an edge e=uv of G, then it becomes local fractional metric dimension (LFMD) dimlfG. In this paper, local fractional and fractional metric dimensions of MOGn are computed for n≅1mod2 in the terms of upper bounds. Moreover, it is obtained that metal organic is one of the graphs that has the same local and fractional metric dimension. |
| format | Article |
| id | doaj-art-2982dede7a2f4b60885ebecefec2fb55 |
| institution | OA Journals |
| issn | 2090-9063 2090-9071 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
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| series | Journal of Chemistry |
| spelling | doaj-art-2982dede7a2f4b60885ebecefec2fb552025-08-20T02:04:01ZengWileyJournal of Chemistry2090-90632090-90712021-01-01202110.1155/2021/55395695539569Computing Bounds of Fractional Metric Dimension of Metal Organic GraphsMohsin Raza0Dalal Awadh Alrowaili1Muhammad Javaid2Khurram Shabbir3Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, College of Science, Jouf University, Sakaka 2014, Saudi ArabiaDepartment of Mathematics, School of Science, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, GC University, Lahore 54000, PakistanMetal organic graphs are hollow structures of metal atoms that are connected by ligands, where metal atoms are represented by the vertices and ligands are referred as edges. A vertex x resolves the vertices u and v of a graph G if du,x≠dv,x. For a pair u,v of vertices of G, Ru,v=x∈VG:dx,u≠dx,v is called its resolving neighbourhood set. For each pair of vertices u and v in VG, if fRu,v≥1, then f from VG to the interval 0,1 is called resolving function. Moreover, for two functions f and g, f is called minimal if f≤g and fv≠gv for at least one v∈VG. The fractional metric dimension (FMD) of G is denoted by dimfG and defined as dimfG=ming:g is a minimal resolving function of G, where g=∑v∈VGgv. If we take a pair of vertices u,v of G as an edge e=uv of G, then it becomes local fractional metric dimension (LFMD) dimlfG. In this paper, local fractional and fractional metric dimensions of MOGn are computed for n≅1mod2 in the terms of upper bounds. Moreover, it is obtained that metal organic is one of the graphs that has the same local and fractional metric dimension.http://dx.doi.org/10.1155/2021/5539569 |
| spellingShingle | Mohsin Raza Dalal Awadh Alrowaili Muhammad Javaid Khurram Shabbir Computing Bounds of Fractional Metric Dimension of Metal Organic Graphs Journal of Chemistry |
| title | Computing Bounds of Fractional Metric Dimension of Metal Organic Graphs |
| title_full | Computing Bounds of Fractional Metric Dimension of Metal Organic Graphs |
| title_fullStr | Computing Bounds of Fractional Metric Dimension of Metal Organic Graphs |
| title_full_unstemmed | Computing Bounds of Fractional Metric Dimension of Metal Organic Graphs |
| title_short | Computing Bounds of Fractional Metric Dimension of Metal Organic Graphs |
| title_sort | computing bounds of fractional metric dimension of metal organic graphs |
| url | http://dx.doi.org/10.1155/2021/5539569 |
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