Geometric and topological properties of the complementary prism networks

Abstract

In this paper, we study the hyperbolicity constant of GG. 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 A(GG) = ∑ uv∈E(GG) a(d u , d v ) and B(GG) = ∑ u∈V(GG) b(d u ) (where d u denotes the degree of the vertex u, a is a symmetric function with real values, and b is a function with real values), and the generalized Wiener index W 𝜆 (GG), of complementary prisms networks. Finally, we performed a numerical study of the generalized Wiener index on random graphs.

Dataset complementary prism networks

“…That is, to generate the complement of a graph, one fills in all the missing edges required to form a complete graph and removes all the edges that were previously there [5] . We would like to point out that 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 [1] . For example, the Petersen graph is a complementary prism, such that (see Fig.…”

“… The dataset offers different topological structures of networks that researchers in the fields of Graph Theory and topological indices can utilize as test instances and benchmarks for evaluating and comparing topological indices. The network topologies and parameters provide in this work can be used for the performance evaluation of lower and upper bounds proposed in the literature for the Wiener Index and Generalized Wiener Index [ 1 , 2 ]. The dataset serves as a basis to generate new datasets, such as generalized complementary prisms [3] , and experimentally evaluated their topological, metric, and/or structural properties.…”

“…The network topologies and parameters provide in this work can be used for the performance evaluation of lower and upper bounds proposed in the literature for the Wiener Index and Generalized Wiener Index [ 1 , 2 ].…”

“…The dataset includes 435 instances of Complementary Prism Networks [1] and the corresponding reference parameters for the networks. Random topologies are provided, with increasing network size (from 12 to 1948 nodes).…”

“…The Excel workbook Experimentos_GGc.xlsx contains two spreadsheets ( Exp_GGc and Graph ). The spreadsheet Exp_GGc aims to collect and summarize the value of the Wiener Index, Generalized Wiener Index [2] , and some lower and upper bounds proposed in [1] for these indices and their percentage error [1] for the instances available in the dataset [6] . The spreadsheet Graph summarizes graphically, in six graphs, the results that were collected in spreadsheet Exp_GGc .…”