On Lanzhou and Ad-hoc Lanzhou Indices of Derived Graphs and Silicate Structures

Degree-based topological indices are among the most widely used descriptors in chemical graph theory. These indices rely on the degrees (or valencies) of the vertices in a molecular graph, where the degree of a vertex corresponds to the number of edges (bonds) connected to it. One among these types of indices is the Lanzhou index, given by Lz(G)=∑a∈V(G)dG(a)2dG¯(a), where dG(a) and dG¯(a) denote the degree of the vertex a in G and the complement graph of G, respectively. Ad-hoc Lanzhou index, Lz¯(G) is obtained by switching the roles of degrees of vertices, i.e., Lz¯(G)=∑a∈V(G)dG(a)dG¯(a)2. In this manuscript, expressions for the Lanzhou and Ad-hoc Lanzhou indices of derived graphs, namely, subdivision, line, vertex semi-total, edge semi-total, and total graphs, are obtained. Also, Lanzhou and Ad-hoc Lanzhou indices of Si2C3-I(s,t),Si2C3-II(s,t), and Si2C3-III(s,t) are obtained and their graphical analysis have been made.