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Investigation of Atom-Bond Connectivity (ABC) Index of
Carbon Nanocones
Lim Pei Xuan
Supervisor: Assoc. Prof. Dr. Roslan Bin Hasni @ Abdullah
Bachelor of Science ( Computational Mathematics )
School of Informatics and Applied Mathematics
A topological index of a chemical graph G is numeric quantity attributed to G. One of the
famous topological indices is atom-bond connectivity (ABC) index, which was proposed
by Ernesto Estrada (1998). ABC index is based on the degrees of vertices of graphs. The
ABC index is defined as follow,
d(u) + d(v) − 2
ABC(G) = ∑ √
d(u)d(v)
uv∈E(G)
where E(G) is the set of edges, whereas d(u) and d(v) are the degree of terminal vertices
u and v of edge uv in G, respectively. In recent years, nanostructures involving carbon
have been the focus of an intense research activity, which is driven to a large extent by
the quest for new materials with specific applications. The simplest example of the
nanostructured carbon is carbon nanocones, which were discovered by Ge and Sattler
(1994). Therefore, the purpose of this project is to investigate ABC index for some simple
graphs and carbon nanocones.
939 | UMT UNDERGRADUATE RESEARCH DAY 2018