Abstract
In recent years, several structurebased properties of the molecular graphs are understood through the chemical graph theory. The molecular graph
1 Introduction
The chemical, physical, and physicochemical properties of a compound, which depends on its structure, can be effectively studied by means of the graph theory. A chemical structure of a compound can be described by a graph
Before proceeding further regarding the definitions of the topological indices studied in this paper, we recall the relevant notions and set the corresponding notations. For the notions and notations not described here we refer [12] to the readers. Throughout this paper, we denote a simple connected graph by
According to the settings described in the previous paragraph, the first KBanhatti index
The modified first KBanhatti index
The first Khyper Banhatti index
The first and secondhyper Revan indices of
where
On the other hand, silicon is a nontoxic semiconductor material that has a very low cost when compared with other materials of the same type. Silicon is a vital part of all electronic devices. The wellconstructed structures of twodimensional (2D) silicon–carbon single layer compounds having different stoichiometric compositions were concluded in ref. [17]. The 2D silicon–carbon single layer may be seen as configurable materials between the pure 2D carbon single layer, graphene, and the pure 2D silicon single layer, silicene. After many attempts, the structure of the SiC sheet (with remarkable stability) was predicted, and for further details about this structure, we refer [18,19,20] to the readers. We consider 2D SiC compounds with a different types of silicon carbide structurebased on lowenergy metastable structures for each silicon, that is,
By keeping in view the importance of the topological indices in theoretical and computational nanosciences, we compute
2 Materials and methods
In Figure 1, the structure of silicon carbide
Figure 1
Figure 2
To compute the topological indices, we defined the partitions of vertices and edges of

Number of edges 


(1, 3)  2  2 
(2, 2) 

2 
(2, 3) 

3 
(3, 3) 

4 
To establish our results, we adopt an approach for combinatorial enrolling, an edge allocate, a vertex portion strategy, enlist hypothetical instruments, and degree counting procedure for vertices and edges. Moreover, we use Matlab and Maple for the estimations, attestation and plotting the obtained results. For further details, see refs. [8,24,25, 26,27].
3 Main results
In this section, we computed the formulas for the first and second KBanhatti, modified KBanhatti, Khyper Banhatti, and hyper Revan indices of silicon carbide
Theorem 1
Let
Proof
Let
Second KBanhatti index of
Theorem 2
Let
Proof
Let
Moreover, from the definition
Theorem 3
Let
Proof
Let
Second Khyper Banhatti index of
Table 2 shows partition of edges of

Number of edges 




2  3  1 


2  2 


2  1 


1  1 
Theorem 4
Let
Proof
Let
Moreover, from the definition of
4 Graphical analysis
In Figure 3, KBanhatti
Figure 3
In Figure 4, modified KBanhatti
Figure 4
In Figure 5, Khyper Banhatti
Figure 5
Figure 6 represents KBanhatti
Figure 6
Figure 7
5 Discussion
In reticular chemistry, it is very difficult to investigate the physicochemical properties and characterization of large chemical structures. However, topological indices are very useful in order to study such properties of large networks. The structural characteristics of the molecules are numerically represented by using the topological indices which may be obtained by applying the theoretical concept on these large networks. In this article, we gave precise formulas of some wellknown topological indices for silicon carbide. In Figures 3–5, we have compared KBanhatti
6 Conclusion and future work
Topological indices are helpful in predicting seeveral physicochemical properties of the chemical compound. The applications of silicon carbide
Acknowledgment
The authors are thankful to the anonymous reviewers for their valuable comments, remarks, and suggestions to improve the quality of the paper.

Funding information: This research was conducted for the fulfillment of job requirement, no external funding was available for this research.

Author contributions: D.Z. – writing, review & editing; M.A.Z. – validation; R.I. – conceptualization, supervision; M.A. – writing, original draft, validation; A.F. – formal analysis, resources; Z.A. – methodology; L.L. – writing, review & editing.

Conflict of interest: Authors state no conflict of interest.

Ethical approval: The conducted research is not related to either human or animal use.

Data availability statement: Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
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