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Atom-Bond Connectivity Index of Graph with Two Edges Added
Fatin Zulaikha Binti Mohd Zainuddin
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), is defined as the
sum of the weight √ d u+d v −2
of all edges uv of G, where d
d u d u (or d v ) denotes the degree of
v
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 two edges are added. As a results, we prove that ABC index of
a graph increase when two edges are added. We end this dissertation by highlighting
some open problems for future investigation.
804 | UMT UNDERGRADUATE RESEARCH DAY 2018