A study of F-coindex for family of unicyclic graphs and dendrimers

Abstract

Topological indices, sometimes also seen as graph-theoretic lters, maintain the order of molecular elements and provide mathematical language to predict features such as boiling points, radius of gyrations, viscosity, etc. These indices re ect topology and are usually mathematically holding xed graph structures. There are certain important categories of topological indices relating to their speci c topological features, such as degrees of vertices, distances between vertices, eccentricities of vertices, communication, etc. In this thesis, we study extremist graphs in relation to certain topological degree attackers. The graphs we emphasize include unicyclic graphs and dendrimers. Our main focus is on studying F-coindex. On smaller graphs the calculation of non-adjacent vertices is easily determined, however, on larger graphs, i.e., n vertices graphs, unicyclic graphs, chemical structures, etc., it is di cult to determine non-adjacent vertexes. First, we develop another F-coindex formula, which directly processes the non-adjacent vertices of large graphs, unicyclic networks, chemical structures, etc. The advantage of the changing formula is that it reduces calculation time and works e ectively on almost every graph. Second, we determine the F-coindex of unicyclic networks, in addition, the minimum and maximum F-coindex of unicyclic networks are also estimated. Finally, we investigate the F-coindex of some dendrimers.