Degree-based topological indices of double graphs and strong double graphs

The topological indices are useful tools to the theoretical chemists that are provided by the graph theory. They correlate certain physicochemical properties such as boiling point, strain energy, stability, etc. of chemical compounds. For a graph G, the double graph D[G] is a graph obtained by taking two copies of graph G and joining each vertex in one copy with the neighbors of corresponding vertex in another copy and strong double graph SD[G] of the graph G is the graph obtained by taking two copies of the graph G and joining each vertex v in one copy with the closed neighborhood of the corresponding vertex in another copy. In this paper, we compute the general sum-connectivity index, general Randić index, geometric-arithmetic index, general first Zagreb index, first and second multiplicative Zagreb indices for double graphs and strong double graphs and derive the exact expressions for these degree-base topological indices for double graphs and strong double graphs in terms of corresponding index of original graph G.