Edge Weight-Based Entropy of Magnesium Iodide Graph

Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk 71491, Saudi Arabia College of Computer Science & Information Technology, Jazan University, Jazan, Saudi Arabia Department of Mathematics, College of Science, Jazan University, New Campus, Jazan 2097, Saudi Arabia Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan


Introduction
Magnesium iodide is a chemical compound and known for its chemical formula Mgl 2 . Magnesium iodide is an inorganic compound that is used for synthesis in various organic substances, as well as it has other commercial uses. e major availability measures of Mgl 2 are having their high impurity and volumes as a submicron and nanopowder. Magnesium iodide is obtained by the combined chemical mixture of hydro-iodic acid and magnesium carbonate and also the major chemical compounds magnesium oxide and magnesium hydroxide can be found. In the major applications of magnesium iodide, it is a highly valuable asset in internal medicine. By a unique pattern of C 4 -graph, the molecular graph of magnesium iodide can be constructed. Having each C 4 -graph inside, multiple heptagons are connected to each other [1]. For the easy readability and better understanding of the molecular graph of magnesium iodide, we labeled the parameters as p is the number of C 4 's of upper sides in a row and q denoted for the count of lower side C 4 in heptagons. For all values of q ∈ Z with q ≥ 1, magnesium iodide graph is needed to maintain for even and odd values of p separately with the relation of p � 2(q + 1) and p � 2q + 1, respectively.
" e entropy of a probability distribution known as a measure of the unpredictability of information content or a measure of the uncertainty of a system." is quotation was the foundation, described in [2], as a seminal theory for the idea of entropy. Due to this concept is strongly based on statistical methodology, it became well-known for chemical structures and their corresponding graphs. is parameter provides a piece of extensive information about graphs, structures, and chemical topologies. In 1955, the notion and its idea were used first time for graphs. In sociology, ecology, biology, chemistry, and in a variety of other technical fields, graph-based entropy or simply entropy has applications [3,4]. Taking into consideration distinct graph elements associated with probability distributions, two types of entropy measurements are determined which are intrinsic and extrinsic entropies. e idea named degree-powers is a mathematical application of applied graph theory towards network theory to investigate networks as information functionals [5,6]. e physical sound of a network associated with the idea of entropy came forward from the authors in [7]. e major concern of this study is to determine some edge weight-based entropies of magnesium iodide structure for both cases of p. e methodology of this study of edge weight-based entropy is defined in Definitions 1-6, with their other fundamentals.

Definition 1.
e first and second Zagreb index is introduced in 1972 by [8,9] as Definition 2. e researcher in [10] introduced the atom bond connectivity index as Definition 3. e geometric arithmetic index of a graph is introduced by [11] as Definition 4. In 2014, entropy for an edge weighted graph F is introduced in [12]: where ψ(uv) is a weight for an edge uv. By letting the edge of weight equal to the main part of the topological index, Manzoor et al. [13,14] introduced the following entropies for an edge weighted-based graph. e following are some important formulas for this research work and all these are based on equation (5).

Definition 5.
e first and second Zagreb entropies are defined as follows [14,15]: Definition 6. e atom bond connectivity and geometric arithmetic entropies are defined as follows [13]: e topic of discussion of this study is closely related to the numerical descriptors or topological indices, so read the fundamentals and basics; we refer to see the recent cluster [16][17][18][19][20][21][22][23]. In the recent decade, this concept has been studied intensively and numerous literatures are available. We will discuss only limited recent most articles on this concept and few are left for the interest of readers [24][25][26][27][28].
To investigate and gain the contents of a network, the entropy formulas as put forward by [2], along with this, it helps to know about the structural information of networks and chemical structures [29]. e concept of edge weightbased entropy of a graph developed the applications and exploration in biological systems. For example, by creating a graph of chemical or any biological system, it has been used to investigate live organisms in the systems. For the biological and chemical applications of this study, see [30,31]. In computer science, in structural chemistry, and in even biology, the entropy can be found by [32]. is entropy, which is also explored in this study document, can be found in [29,33] in-network heterogeneity work. In more recent literature about edge weight-based entropy, one can find [34,35]. e edge weight-based entropies of the first and second Zagreb index, atom bond connectivity index, and geometric arithmetic index are figured out for the magnesium iodide or Mgl 2 structure, for both even and odd cases of parameter p.
e topological index of the magnesium iodide or Mgl 2 structure, for both even and odd cases of parameter p, are computed in [1]. We will use the results of theorems from [1], which are summarized in Tables 1 and 2. Moreover, due to long expressions of theorems, we reduced the calculations up to four decimal digits.

Results on the Edge Weight-Based Entropy of Magnesium Iodide
Given in this section are some important results of this research work. e idea is totally dependent on the structural values of Mgl 2 or magnesium iodide graph, which is defined in Table 3 (for p � odd and Table 4 (for p � even, and the structure is shown in Figure 1.
For the odd values of p with given q ≥ 1, let p � 2q + 1 and q ∈ Z.

(16)
Proof. Using the value of geometric arithmetic topological index from Table 1, along with the edge types from Table 3, in the formula defined in equation (9), after simplification, the entropy of geometric arithmetic resulted in □ Case 2. For the even values of p with given q ≥ 1, let p � 2(q + 1) and q ∈ Z.
Proof. Using the value of atom bond connectivity topological index from Table 2, along with the edge types from Proof. Using the value of geometric arithmetic topological index from Table 2, along with the edge types from Table 4, in the formula defined in equation (9)

Conclusion
e edge weight-based entropy of a network or structure provides structural information and detailed content in the form of mathematical equations. To add up some structural information and properties of magnesium iodide or Mgl 2 structure, we determined the edge weight-based entropies of the first and second Zagreb index, atom bond connectivity index, and geometric arithmetic index. e results carried information for both even and odd cases of parameter p, of magnesium iodide, or Mgl 2 structure.

Data Availability
ere are no data associated with this article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.