D-ANTIMAGIC LABELING ON ORIENTED GRAPHS
Let ??G be an oriented graph with vertex set V ( ??G ) and arc set A( ??G ). Suppose that D ? {0, 1, 2, . . . , ?} is a distance set where ? = max{d(u, v) < ?|u, v ? V ( ??G )}. Given a bijection h : V ( ??G ) ? {1, 2, , . . . , |V ( ??G )|}, the D-neighborhood weight of a vertex v ? V (...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/74548 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let
??G be an oriented graph with vertex set V (
??G ) and arc set A(
??G ). Suppose that
D ? {0, 1, 2, . . . , ?} is a distance set where ? = max{d(u, v) < ?|u, v ? V (
??G )}.
Given a bijection h : V (
??G ) ? {1, 2, , . . . , |V (
??G )|}, the D-neighborhood
weight of a vertex v ? V (
??G ) is defined as ?D(v) =
P
u?ND(v) h(u), where
ND(v) = {u ? V |d(v, u) ? D}. A labeling h is called a D-antimagic labeling if
for every pair of distinct vertices x and y, ?D(x) ?= ?D(y). An oriented graph
??G is
called D-antimagic if
??G contains such labeling.
In this thesis, we study the existences and characteristics of orientations on paths,
cycles, complete bipartite graphs, and complete multipartite graphs such that those
graphs admit D-antimagic labelings. |
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