Characterizing Interconnection Networks in Terms of Complexity via Entropy Measures

Abstract

One of the most recent advancements in graph theory is the use of a multidisciplinary approach to the investigation of specific structural dependent features, such as physico-chemical properties, biological activity and the entropy measure of a graph representing objects like a network or a chemical compound. The ability of entropy measures to determine both the certainty and uncertainty about objects makes them one of the most investigated topics in science along with its multidisciplinary nature. As a result, many formulae, based on vertices, edges and symmetry, for determining the entropy of graphs have been developed and investigated in the field of graph theory. These measures assist in understanding the characteristics of graphs, such as the complexity of the networks or graphs, which may be determined using entropy measures. In this paper, we derive formulae of entropy measures of an extensively studied family of the interconnection networks and classify them in terms of complexity. This is accomplished by utilizing all three tools, including analytical formulae, graphical methods and numerical tables.

Exploring Novel Topological Descriptors: Geometric-Harmonic and Harmonic-Geometric Descriptors for HAC and HAP Conjugates

“…9n − 2 (6,8) 10n − 2 (6, 9)(6, 10) n (7, 7) 5n (7, 8)(7, 10) 4n (8,8) 4n − 1 (8, 10)(9, 10) 3n (10,11) 2n…”

“…Chemists commonly employ quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) methodologies [1][2][3][4] to streamline the evaluation of the biological, physical, and chemical properties of myriad newly developed nanomaterials, crystalline substances, and drugs. Topological indices (TIs), or numerical invariants, constitute a crucial tool within QSPR and QSAR analyses [5][6][7][8][9]. These indices are usually described as numbers that are linked to the chemical structure.…”

The Chromatic Entropy of Linear Supertrees and Its Application

“…Based on Shannon entropy and some graph variables, many graph entropies were proposed; we refer to the reader to [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For graph entropy, there are lots of applications in chemistry, network, biology and so on; we refer to the reader to [16][17][18][19][20][21][22][23].…”