Research Article On Chemical Invariants of Semitotal-Point Graph and Its Line Structure of the Acyclic Kragujevac Network: A Novel Mathematical Analysis Salma Kanwal, 1 Rabia Safdar , 1 AsiaRauf, 2 Ammara Afzal, 1 Wasim Jamshed , 3 Meznah M. Alanazi, 4 andH.Y.Zahran 5,6 1 Department of Mathematics, Lahore College for Women University, Lahore 54000, Pakistan 2 Department of Mathematics, Lahore College for Women University, Faisalabad 38000, Pakistan 3 Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad 44000, Pakistan 4 Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia 5 Laboratory of Nano-Smart Materials for Science and Technology (LNSMST), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia 6 Nanoscience Laboratory for Environmental and Biomedical Applications (NLEBA), Metallurgical Lab.1, Department of Physics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt Correspondence should be addressed to Rabia Safdar; rabia.safdar1109@gmail.com and Wasim Jamshed; wasiktk@hotmail.com Received 29 November 2021; Accepted 19 January 2022; Published 22 February 2022 Academic Editor: Haidar Ali Copyright © 2022 Salma Kanwal et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Acyclic Kragujevac network is denoted by K; K ∈ Kg q�r(2s+1)+1,r . In this article, we have taken a deep look at some of the topological properties of the semitotal-point graph as well as its line structure by computing some algebraic polynomials. Few degree-dependent chemical invariants that can primarily be obtained via these algebraic expressions are also put forward. 1.Introduction A topological index, also known as a connectivity index, is a sort of molecular descriptor that is computed based on the chemical graph of a chemical compound in the fields of chemical graph theory, molecular topology, and mathematical chemistry. Topological indices are nu- merical factors that define the topology of a graph and are typically graph invariants. Topological indices are used in the progress of quantitative structure-activity relation- ships (QSARs), which correspond to biological activity or other characteristics of molecules with their chemical composition. e graphs under consideration in the following work are undirected, lack loops, as well as have bounded sets of nodes and edges. Let V(L) and E(L) indicate the node and line sets for graph L, respectively. Moreover, the cardinality of lines attached to a point denoted as d L (u) for u is its degree. Let R 2 ,R 3 ,R 4 , ... be the rooted trees whose structure is shown in Figure 1. Another Kragujevac tree K from class Kg 29,4 is shown in Figure 2. A tree [1–7] consisting of a central vertex of degree not less than 3 and rooted trees of the form R 1 ,R 2 ,R 3 , ... are joined to that tree is called a proper Kragujevac tree. Kg q,r denotes the class of proper Kragujevac trees K of order q and a central vertex with degree r. A tree derived by placing a new degree 2 node to a line linked to the degree one node of some proper acyclic Kragujevac network is termed as im- proper acyclic Kragujevac network, specified by Kg ∗ q,r . e rooted trees linked to the main vertex are specified as R t 1 ,R t 2 , ... ,R t r where t i ≥ 2; i � 1, ... ,r. Here in this work, a unique case of the acyclic Kragujevac network is under consideration when R t 1 ,R t 2 , ..., R t r are isomorphic, i.e., t 1 � t 2 � ... � t r � s. erefore, in this case, this structure Hindawi Journal of Chemistry Volume 2022, Article ID 7995704, 20 pages https://doi.org/10.1155/2022/7995704