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Exploration of Friendly Index Set
S’ng Yuan Nian
Supervisor: Assoc. Prof. Dr. Roslan Bin Hasni @ Abdullah
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
Let G = (V, E) be a graph, where V be the vertex set, E be the edge set and let A be an
abelian group. A labelling f: V → A that induces an edge labeling f ∗: E → A defined by
f ∗ (xy) = f(x) + f(y). For I ∈ A, v f(i)
= card{v ∈ V: f(v) = i} and e f (i) = card{e ∈
E: f ∗ (e) = i}. For all (i, j) ∈ A × A, a labelling f of a given graph G is said to be A-friendly
if |vf(i) − vf(j)| ≤ 1 . When A = Z2, the set FI(G) = {| ef (1) - ef (0)| : f is friendly} is
defined as the friendly index set of G. In this paper, we analyse the concept of friendly
index set in path, complete, 2-regular, books, edge-gluing and bipartite graphs and
determined which of them admit in friendly index set.
1005 | UMT UNDERGRADUATE RESEARCH DAY 2018