Browsing by Author "Nadeem, Muhammad Faisal"

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Bounds on Partition Dimension of Peterson Graphs
(Taylor & Francis Ltd, 2021) Khalaf, Abdul Jalil M.; Nadeem, Muhammad Faisal; Azeem, Muhammasd; Cancan, Murat; Farahani, Mohammad Reza
The distance of a connected, simple graph P is denoted by d(eta(1), eta(2)), which is the length of a shortest path between the vertices eta(1), eta(2) is an element of V(P), where V(P) is the vertex set of P. The l- ordered partition of V(P) is theta = (theta(1), theta(2), ..., theta(t)}. A vertex eta is an element of V(P), and r(eta vertical bar theta) = {d(eta, theta(1)), d(eta, theta(2)), ...., d(eta, theta(t))} be a l - tuple distances, where r(eta vertical bar theta) is the representation of a vertex eta with respect to set theta. If r(eta vertical bar theta) of eta is unique, for every pair of vertices, then theta is the resolving partition set of V(P). The minimum number l in the resolving partition set theta is known as partition dimension (pd(P)). In this paper, we studied the generalized families of Peterson graph, P-lambda,P-lambda-1 and proved that these families have bounded partition dimension.
On Degree Based Topological Indices of Transition Metal-Tetra Cyano Polycyclic Benzene Organic Network
(Taylor & Francis Ltd, 2022) Zhao, Weidong; Nadeem, Muhammad Faisal; Cancan, Murat; Siddiqui, Muhammad Kamran; Ali, Kashif; Siddiqui, Hafiz Muhammad Afzal; Kanwal, Salma
In this paper, we discuss the degree based topological properties of the novel planar metal-organic networks TM - TCNB. Interestingly, the TM - TCNB systems are metallic in any event in one turn heading and show long-run ferromagnetic coupling on the off chance that for attractive structures, which speak to perfect applicants and a fascinating possibility of uncommon applications in spintronics. Chemical graph theory plays an important role in modeling and designing any chemical structure. The topological indices are the numerical invariants of a molecular graph and are very useful for predicting their physical properties. We have computed the degree based topological indices for this metal-organic networks TM - TCNB.