Browsing by Author "Khalaf, A.J.M."

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Degree-Based Topological Indices and Polynomials of Cellulose
(Abdus Salam School of mathematical Sciences, 2021) Khalaf, A.J.M.; Shanmukha, M.C.; Usha, A.; Shilpa, K.C.; Cancan, M.
This work attempts to compute cellulose's chemical structure using topological indices based on the degree and its neighbourhood. The study of graphs using chemistry attracts a lot of researchers globally because of its enormous applications. One such application is discussed in this work, where the structure of cellulose is considered for which the computation of topological indices and analysis of the same are carried out. A polymer is a repeated chain of the same molecule stuck together. Glucose is a natural polymer also called, Polysaccharide. The diet of the humans include fibre which contains cellulose but direct consumption of the same may not be digestible by them. © 2021. All Rights Reserved.
Nature of Graphs of Commutative Ring of Gaussian Integer Modulo N Under X3 - 1 Mapping
(Abdus Salam School of mathematical Sciences, 2021) Khalaf, A.J.M.; Nazeer, S.; Qayyum, K.; Cancan, M.
The aim of the present paper is to observe the structures of digraphs derived from the mappings f1: Zn[i] Zn[i] defined by f1 (x) = x3 — 1 whose vertex is Zn[i] = {a + bi: a, b (Formula presented) Zn} and for which there is a directed edge from x (Formula presented) Zn[i] to y (Formula presented) Zn[i] if and only if x3 — 1 = y (mod n). In this article, we investigated the structure of digraph. The in-degree of 1 and 0 in D1(n) are established where D1(n) is digraph obtained. Some regularity conditions of D1(n) are also discussed. For certain values of n, the simple conditions for the number of components and length of cycles is obtained. © 2021. All Rights Reserved.
Partition Dimension of Generalized Peterson and Harary Graphs
(Abdus Salam School of mathematical Sciences, 2021) Khalaf, A.J.M.; Nadeem, M.F.; Azeem, M.; Farahani, M.R.; Cancan, M.
The distance of a connected, simple graph (Formula presented) is denoted by d(α1, α2), which is the length of a shortest path between the vertices α1,α2 (Formula presented) V((Formula presented)), where V((Formula presented)) is the vertex set of (Formula presented). The l-ordered partition of V((Formula presented)) is K = {K1, K2,..., Kl}. A vertex α (Formula presented) V((Formula presented)), and r(α|K) = {d(α, K1), d(α, K2),..., d(α, Kl)} be a l-tuple distances, where r(α|K) is the representation of a vertex a with respect to set K. If r(a|K) of a is unique, for every pair of vertices, then K is the resolving partition set of V((Formula presented)). The minimum number l in the resolving partition set K is known as partition dimension (pd(P)). In this paper, we studied the generalized families of Peterson graph, Pλx and proved that these families have bounded partition dimension. © 2021. All Rights Reserved.
Reversed Degree-Based Topological Indices for Benzenoid Systems
(Abdus Salam School of mathematical Sciences, 2021) Khalaf, A.J.M.; Virk, A.U.R.; Ali, A.; Cancan, M.
Topological indices are numerical values that correlate the chemical structures with physical properties. In this article, we compute some reverse topological indices namely reverse Atom-bond connectivity index and reverse Geometric-arithmetic index for four different types of Benzenoid systems. © 2021. All Rights Reserved.