shahbaz ali

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Hi!I'm Dr. Shahbaz Ali working in the department of Mathematics, the Islamia University of Bahawalpur, Rahim Yar Khan Campus, Pakistan. I have completed my Ph.D in the field of number theory and graph theory. I have published more than 45 research articles in well reputated journals. Best regards,Dr. Shahbaz Ali

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New Labeling Algorithm on Various Classes of Graphs with Applications

2019 International Conference on Innovative Computing (ICIC)

In order to develop an algorithm, computer theories are essential and often used in a mathematica... more In order to develop an algorithm, computer theories are essential and often used in a mathematical sequence. Most of them without sufficient mathematics are difficult to understand. A mathematical algorithm is, therefore, a better guide to confirm whether or not a software is correct. This implies that a mathematical knowledge-based algorithm is of great concern. Let <tex>$S=\{r_{1},\ r_{2},\ \cdots r_{\varphi(n)}\}$</tex> be a set of all co-prime residues of a positive integer <tex>$n$</tex>. An integer <tex>$n > 0$</tex> is termed as totient if the sum of co-prime residues of <tex>$n$</tex> is <tex>$2^{k}n, k\geq 1$</tex>. A graph <tex>$G$</tex> with <tex>$V$</tex> and <tex>$E$</tex> be the set of vertices and edges of <tex>$G$</tex> respectively, then <tex>$G$</tex> is said to be a totient graph if there exists a one-one function <tex>$h:V\rightarrow N$</tex>, whose induced function <tex>$h^{*}:E\rightarrow N$</tex>, defined by <tex>$f^{*}(ab)=f(a)f(b)$</tex> assigns a totient number for each edge of <tex>$G$</tex>. In this piece of work, we propose new labeling algorithms for several classes of graphs.

Hex-Derived Molecular Descriptors via Generalized Valency-Based Entropies

IEEE Access

Entropy is a thermodynamic function in chemistry that, based on the number of possible configurat... more Entropy is a thermodynamic function in chemistry that, based on the number of possible configurations for a given system or process, measures the randomness and disorder of molecules in that system or process. Many problems in arithmetic, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. A topological descriptor also connects certain physical aspects of the underlying chemical substances, in contrast to a topological index, which in chemical graph theory is a numerical representation of a chemical network. When building models for any chemical network, the graph is crucial. Simonraj et al. produced a brand-new category of graphs known as the third kind of hex-derived networks. In our work, we discuss the third class of hex-derived networks, which includes hex-derived networks (HDN 3), triangular hex-derived networks (T HDN 3), rectangular hex-derived networks (RHDN 3), and chain hex-derived networks (CHDN 3). We compute exact results for newly defined entropies by utilizing their topological indices based on end vertex degrees. INDEX TERMS Hex-derived network (HDN 3), triangular hex-derived network (T HDN 3), rectangular hex-derived network (RHDN 3) and chain hex-derived network CHDN 3).

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