Browsing by Author "Haidar, Ghulam"

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Constant time calculation of the metric dimension of the join of path graphs

Zhang, Chuanjun; Haidar, Ghulam; Khan, Murad ul Islam; Yousafzai, Faisal; Hila, Kostaq; Khan, Asad ul Islam. (MDPI, 2023)

The distance between two vertices of a simple connected graph G, denoted as (Formula presented.), is the length of the shortest path from u to v and is always symmetrical. An ordered subset (Formula presented.) of (Formula ...
Metric dimensions of bicyclic graphs

Khan, Asad ul Islam; Haidar, Ghulam; Abbas, Naeem; Khan, Murad ul Islam; Niazi, Azmat Ullah Khan; Khan, Asad ul Islam. (MDPI, 2023)

The distance d(va, vb) between two vertices of a simple connected graph G is the length of the shortest path between va and vb. Vertices va, vb of G are considered to be resolved by a vertex v if d(va, v) 6= d(vb, v). An ...