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The Effect of Geometric-Arithmetic Index of Graph with Three Edge Added
Nurfadillah Binti Che Musa
Supervisor: Dr. Mohamad Nazri Bin Husin
Bachelor of Science (Financial Mathematics)
School of Informatics and Applied Mathematics
The concept of geometric-arithmetic (GA) index was put forward in chemical graph theory
recently. Furthermore, several works has already appeared dealing with this index.
Namely, these are obtained from the ratio of geometric and arithmetic means of some
properties of adjacent vertices. The first GA index was proposed by Vukičević and was
simply named “geometric-arithmetic index”. It’s define as GA(G) = ∑
√d 1 d 2
v i v j 1
2 (d i+d j )
. The
purpose of this dissertation is to explain the concept of GA index. Besides that, we also
investigate the effect of GA index when three edges are added into the underlying graph.
As a result, we prove that the GA index increase when three edges added into the
underlying graph. We end this dissertation by highlighting some open problem for the
further investigation.
867 | UMT UNDERGRADUATE RESEARCH DAY 2018