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The Investigation of Super Graceful Labeling in Graph
Pang Poh Feng
Supervisor: Assoc. Prof. Dr. Roslan Bin Hasni @ Abdullah
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
Let G = (V(G), E(G)) be an undirected graph with order p and size q. A bijection
f ∶ V(G) ∪ E(G) → {1, 2, 3, … , p + q} such that f(uv) = |f(u) − f(v)| for every edge uv ∈
E(G) is a super graceful labeling. G is a super graceful graph if it admits super graceful
labeling. In this study, we verified the super gracefulness of path graph, cycle graph,
complete graph, the complete tripartite graphs K(1, 1, r) and some disjoint union graphs.
We figured out the trend to label some of the graphs and it is discussed in this paper. We
also apply three construction methods C1, C2 and C3 introduced by Lau et al. (2016) to
those super graceful graphs to get new super graceful graphs. The construction C4 is
verified with examples to show that it creates super graceful bipartite graph.
1001 | UMT UNDERGRADUATE RESEARCH DAY 2018