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Atom-Bond Connectivity Index of Graph with
Three Edges Deleted
Nur Azila Binti Zawawi
Supervisor: Dr. Mohamad Nazri Bin Husin
Bachelor of Science (Financial Mathematics)
School of Informatics and Applied Mathematics
The Atom-Bond Connectivity index of a graph G, denoted as ABC(G) was proposed by
Ernesto Estrada et al. ABC index is defined as the sum of the weight √ d u + d v −2
d u d v
of all
edges uv of G, where du (or dv) denotes the degree of vertex u (or v) in G. The ABC
index provides a good model for the stability of linear and branches alkanes as well as
the strain energy of cycloalkanes. The purpose of this dissertation is to explain the
concept of ABC index. Besides that, we also investigate the effect of ABC index when
three edges are deleted. As a results we prove that the ABC index of graph decrease. We
end this dissertation by highlighting some open problems for further investigation.
856 | UMT UNDERGRADUATE RESEARCH DAY 2018