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.
