The use of silicon carbide is increasing significantly in the fields of research and technology. Topological indices enable data gathering on algebraic graphs and provide a mathematical framework for analyzing the chemical structural characteristics. In this paper, well-known degree-based topological indices are used to analyze the chemical structures of silicon carbides. To evaluate the features of various chemical or non-chemical networks, a variety of topological indices are defined. In this paper, a new concept related to the degree of the graph called "bi-distance" is introduced, which is used to calculate all the additive as well as multiplicative degree-based indices for the isomer of silicon carbide, Si2C3-1[t, h]. The term "bi-distance" is derived from the concepts of degree and distance in such a way that second distance can be used to calculate degree-based topological indices.

This work aims to study the extent of the association between the numbers of COVID-19 infections among the regions of Saudi Arabia using a graph theory, especially the calculation of the minimum spanning tree. The research also aims mainly to classify the central regions of Saudi Arabia, whose number of COVID-19 virus infections is centrally linked to other provinces, i.e., when the number of infections in these central regions increases, the number of infections in the associated regions increases and when infections decrease in these central regions, infections decrease in the associated regions.