Topology Of Fullerenes

TOPOLOGY OF FULLERENES Introduction Fullerenes are defined as carbon molecules that form polyhedral cages. There exists a close connection between structural chemistry and the graph theory in pursuing the topology of fullerene. The proposal report seeks to expound on the importance and the objective of the study of the topology of fullerene. The report consists of a brief preview of the previous studies of the study topic. The scope that the study will be able to achieve with the time constraints is also stipulated in the proposal report. The most considered direct graphical description is a sequence of numbers, as a connection table, sometimes topological index (single derived number), a polynomial or a matrix. In the graph theory, the finite series such as the series of numbers of independent k edge sets or the distance degree sequence or are described by polynomials counting (Cataldo et al., 2011) PG,x=kpG,k .xk In this case: pG,x is the occurence frequency of the property G partions k-is the length x is the k holding parameterFullerenes are defined as polyhedral cages forming carbon molecules. Their structure of bond exhibit cubic planar graphs that contain only hexagon and pentagon faces. This dissertation will focus on the planar graphs mathematics that has been used to present the fullerene graphs as studied by Goldberg and Coxeter (Cataldo et al., 2011). In this paper, there will be a wide description of the previous topological and graph theories which have been used in the research of fullerenes. The study will…

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