D-ANTIMAGIC LABELING FOR HYPERCUBES
Let G = (V;E) be a graph with order n, and let f : V (G) ! f1; 2; :::; ng be a bijection. Define a distance set, D f0; 1; 2; : : : ; diam(G)g. For each vertex v 2 V (G), the sum of its D-neighborhood labels u2ND(v)f(u) is called as the D- weight of v denoted by wD(v). If wD(x) 6= wD(y), for each...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/46381 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let G = (V;E) be a graph with order n, and let f : V (G) ! f1; 2; :::; ng be
a bijection. Define a distance set, D f0; 1; 2; : : : ; diam(G)g. For each vertex
v 2 V (G), the sum of its D-neighborhood labels u2ND(v)f(u) is called as the D-
weight of v denoted by wD(v). If wD(x) 6= wD(y), for each two distinct vertices x
and y, then f is also called as D-antimagic labeling.
The objective of this thesis is to find various distance sets D such that a hypercube
admits a D-antimagic labeling. Our method is by recursively constructing
D-antimagic labelings based on a labeling for hypercubes with smaller dimension.
We also construct an algorithm to determine all distance sets D such that a graph G
admits a D-antimagic labelling.
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