Computing Some Degree-Based Topological Indices of Honeycomb Networks

A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network O X n , silicate network S L n , chain silicate network C S n , and hexagonal network H X n . Also, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for honeycomb network H C n .

Global Connectivity and Ethnic Fractionalization: New Frontiers of Global Trade Agenda

International trade is an exchange that involves goods and services between countries or international territories, and it signifies a significant share of gross domestic product. Global trading provides opportunities for the country to show its products and services through imports and exports. While this international event gives rise to a world economy, global connectivity and ethnic heterogeneity play a significant role. This paper aims to determine whether the ruggedness of a country supports international trade and global connectivity and whether the ruggedness of ethnic heterogeneity supports global trading. This paper uses the non-experimental quantitative inferential design utilizing Fractal Analysis to determine the self-similarity of countries engaging in international trade in terms of their global connectivity index and ethnic fractionalization. The International Trade data provided by the World Integrated Trade Solutions and the Global Connectivity Index (GCI) data through Huawei Technologies are plotted in a histogram through Minitab Software to determine the fractality and further apply exponential logarithm. Study shows that global connectivity and ethnic fractionalization induce the fractal characteristics of the countries’ international trade ruggedness. Specific to the behavior is that countries with very high international trade also behave similarly with high global connectivity and very low ethnicity fractionalization. As countries sustain a progressive economic stance, their societies maintain very few ethnic groups to promote social cohesion, much less conflict created by many ethnic groups that vary in their concerns. This paper further explains that only countries with digital economic competitiveness and cultural homogeneity survive robust international trade.

Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1 and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

Topological Descriptors of M-Carbon M r , s , t

We have studied topological indices of the one the hardest crystal structures in a given chemical system, namely, M-carbon. These structures are based and obtained by the famous algorithm USPEX. The computations and applications of topological indices in the study of chemical structures is growing exponentially. Our aim in this article is to compare and compute some well-known topological indices based on degree and sum of degrees, namely, general Randić indices, Zagreb indices, atom bond connectivity index, geometric arithmetic index, new Zagreb indices, fourth atom bond connectivity index, fifth geometric arithmetic index, and Sanskruti index of the M-carbon M r , s , t . Moreover, we have also computed closed formulas for these indices.

Connectivity Index of M-polar Fuzzy Graph with Application

This paper brings in connectivity index of a m -polar fuzzy graph ( m PFG) with its boundedness. We investigate how the connectivity index of a m PFG changes when a vertex or an edge is deleted. Some special types of vertices include m -polar fuzzy connectivity enhancing node( m PFCEN), m -polar fuzzy connectivity neutral node ( m PFCNN), m -polar fuzzy connectivity reducing node ( m PFCRN) with their properties are discussed.

Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers

A parameter is a numerical factor whose values help us to identify a system. Connectivity parameters are essential in the analysis of connectivity of various kinds of networks. In graphs, the strength of a cycle is always one. But, in a fuzzy incidence graph (FIG), the strengths of cycles may vary even for a given pair of vertices. Cyclic reachability is an attribute that decides the overall connectedness of any network. In graph the cycle connectivity (CC) from vertex a to vertex b and from vertex b to vertex a is always one. In fuzzy graph (FG) the CC from vertex a to vertex b and from vertex b to vertex a is always same. But if someone is interested in finding CC from vertex a to an edge ab, then graphs and FGs cannot answer this question. Therefore, in this research article, we proposed the idea of CC for FIG. Because in FIG, we can find CC from vertex a to vertex b and also from vertex a to an edge ab. Also, we proposed the idea of CC of fuzzy incidence cycles (FICs) and complete fuzzy incidence graphs (CFIGs). The fuzzy incidence cyclic cut-vertex, fuzzy incidence cyclic bridge, and fuzzy incidence cyclic cut pair are established. A condition for CFIG to have fuzzy incidence cyclic cut-vertex is examined. Cyclic connectivity index and average cyclic connectivity index of FIG are also investigated. Three different types of vertices, such as cyclic connectivity increasing vertex, cyclically neutral vertex and, cyclic connectivity decreasing vertex, are also defined. The real-life applications of CC of FIG in a highway system of different cities to minimize road accidents and a computer network to find the best computers among all other computers are also provided.

Sharp Lower Bounds of the Sum-Connectivity Index of Unicyclic Graphs

The sum-connectivity index of a graph G is defined as the sum of weights 1 / d u + d v over all edges u v of G , where d u and d v are the degrees of the vertices u and v in graph G , respectively. In this paper, we give a sharp lower bound on the sum-connectivity index unicyclic graphs of order n ≥ 7 and diameter D G ≥ 5 .