Geometric and topological properties of the complementary prism networks

The complementary prism of , denoted by , is the graph obtained from the disjoint union of and by adding edges between the corresponding vertices of and . In this paper, we study the hyperbolicity constant of . In particular, we obtain upper and lower bounds for the hyperbolicity constant, and we compute its precise value for many graphs. Moreover, we obtain bounds and closed formulas for the general topological indices and (where denotes the degree of the vertex is a symmetric function with real values, and is a function with real values), and the generalized Wiener index , of complementary prisms networks. Finally, we performed a numerical study of the generalized Wiener index on random graphs.