Muhammad Shafiq

Bio: Muhammad Shafiq is an academic researcher from Government College University, Faisalabad. The author has contributed to research in topics: Ring (chemistry) & Dihedral angle. The author has an hindex of 9, co-authored 86 publications receiving 363 citations. Previous affiliations of Muhammad Shafiq include University of Management and Technology & Yahoo!.

On the metric dimension of Mobius ladders

Abstract: If G is a connected graph, the distance d(u, v) between two vertices u, v is an element of V(G) is the length of a shortest path between them. Let W = {w(1), w(2), ... , w(k)} be an ordered set of vertices of G and let v be a vertex of G. The representation r(v vertical bar W) of v with respect to W is the k-tuple (d(v, w(1)), d(v, w(2)), ... , d(v, w(k))). If distinct vertices of G have distinct representations with respect to W, then W is called a resolving set or locating set for G. A resolving set of minimum cardinality is called a basis for G and this cardinality is the metric dimension of G, denoted by dim(G). A family G of connected graphs is a family with constant metric dimension if dim(G) does not depend upon the choice of G in G. In this paper, we are dealing with the study of metric dimension of Mobius ladders. We prove that Mobius ladder M-n constitute a family of cubic graphs with constant metric dimension and only three vertices suffice to resolve all the vertices of Mobius ladder M-n except when n equivalent to 2(mod 8). It is natural to ask for the characterization of regular graphs with constant metric dimension.

Synthesis of novel anti-bacterial 2,1-benzothiazine 2,2-dioxides derived from methyl anthranilate

Abstract: A convenient ultrasound assisted synthesis of new anti-bacterial N-benzylidene-N’-(1-methyl-2, 2-dioxo-2,3-dihydro-1H-2λ6-benzo[c][1,2]thiazin-4-ylidene)hydrazines from methyl anthranilate is reported. Methyl anthranilate was reacted with methane sulfonyl chloride, followed by N-alkylation and subsequent base catalyzed cyclization. Hydrazinolysis of the cyclized products followed by their ultrasound mediated condensations with different benzaldehydes yielded the title compounds. Some of these compounds showed good anti-bacterial activity against Pseudomonas aeruginosa, Salmonella typhimurium and Staphylococcus aureus.

On Metric Dimension of Generalized Petersen Graphs P(n, 3).

Abstract: In this paper we study the metric dimension of the generalized Petersen graphs P (n, 3) by giving a partial answer to an open problem raised in [8]: Is P (n, m) for n ≥ 7 and 3 ≤ m ≤ bn−1 2 c, a family of graphs with constant metric dimension? We prove that the generalized Petersen graphs P (n, 3) have metric dimension equal to 3 for n ≡1(mod 6), n ≥ 25, and to 4 for n ≡ 0(mod 6), n ≥ 24. For the remaining cases only 4 vertices appropriately chosen suffice to resolve all the vertices of P (n, 3), thus implying that dim(P (n, 3)) ≤ 4, except when n ≡ 2(mod 6), when dim(P (n, 3)) ≤ 5.

On the Degree-Based Topological Indices of Some Derived Networks

Abstract: There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physical chemical properties of primary chemical compounds. The biological activity of chemical compounds can be constructed by the help of topological indices. In theoretical chemistry, numerous chemical indices have been invented, such as the Zagreb index, the Randic index, the Wiener index, and many more. Hex-derived networks have an assortment of valuable applications in drug store, hardware, and systems administration. In this analysis, we compute the Forgotten index and Balaban index, and reclassified the Zagreb indices, A B C 4 index, and G A 5 index for the third type of hex-derived networks theoretically.

A Dynamic Survey of Graph Labeling

Abstract: A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

Arsenic sensor development based on modification with (E)-N′-(2-nitrobenzylidine)-benzenesulfonohydrazide: a real sample analysis

Abstract: (E)-N′-(2-Nitrobenzylidene)-benzenesulfonohydrazide (NBBSH) was prepared from 2-nitrobenzaldehyde and benzenesulfonylhydrazine by using a simple condensation process with medium yield. It was then crystallized in methanol and characterized using various spectroscopic techniques such as Fourier transform infra-red spectroscopy (FTIR), ultra-violet visible spectroscopy (UV-vis), proton nuclear magnetic resonance (1H-NMR), X-ray photoelectron spectroscopy (XPS), and carbon-13 nuclear magnetic resonance (13C-NMR). The structure of the NBBSH molecule was confirmed using the single crystal X-ray diffraction technique (SCXRDT). A thin layer of NBBSH slurry was deposited onto a cleaned and dried flat round surface of GCE with a binding agent (Nafion) to fabricate a sensitive and selective heavy metal ion (HMI) sensor. The fabricated NBBSH/GCE sensor exhibited enhanced sensing performances such as sensitivity, limit of detection (LOD), linear dynamic range (LDR), and long-term stability towards selective arsenic ions. The calibration curve (CC) was found to be linear over a broad range of As3+ conc. (0.1 nM–0.1 M) and the calculated sensitivity and LOD (based on 3N/S) were found to be ∼190.0 pA μM−1 cm−2 and 50.0 pM, respectively. This novel approach can be used as an efficient path for the development of HMI sensors regarding monitoring of hazardous materials in biological and environmental sciences.