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Geometric and topological properties of the complementary prism networks

Abstract:

The complementary prism of (Formula presented.), denoted by (Formula presented.), is the graph obtained from the disjoint union of (Formula presented.) and (Formula presented.) by adding edges between the corresponding vertices of (Formula presented.) and (Formula presented.). In this paper, we study the hyperbolicity constant of (Formula presented.). 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 (Formula presented.) and (Formula presented.) (where (Formula presented.) denotes the degree of the vertex (Formula presented.) is a symmetric function with real values, and (Formula presented.) is a function with real values), and the generalized Wiener index (Formula presented.), of complementary prisms networks. Finally, we performed a numerical study of the generalized Wiener index on random graphs.