SOME CLASSES OF D-ANTIMAGIC GRAPHS
In 2013, Kamatchi and Arumugam introduced the concept of a distance antimagic graph. A simple graph G is said to be distance antimagic if there is a bijection f : V (G) ? {1, 2, . . . , |V (G)|} such that for every x, y ? V (G) with x ?= y applies w(x) ?= w(y) where w(x) = P z?N(x) f(z) and N(x...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/65076 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | In 2013, Kamatchi and Arumugam introduced the concept of a distance antimagic
graph. A simple graph G is said to be distance antimagic if there is a bijection
f : V (G) ? {1, 2, . . . , |V (G)|} such that for every x, y ? V (G) with x ?= y applies
w(x) ?= w(y) where w(x) =
P
z?N(x) f(z) and N(x) = {z|(x, z) ? E(G)}. If
{w(x)|x ? V (G)} = {a, a + d, . . . , a + (n ? 1)d}, then G is called (a, d)-distance
antimagic.
In 2021, Simanjuntak et. al. generalized the concept of distance antimagic into
D-antimagic. Suppose that G is a simple graph with diameter d and D is a nonempty
subset of {0, 1, 2, . . . , d}. A graph G is called aD-antimagic graph if there is
a bijection g : V (G) ? {1, 2, . . . , |V (G)|} such that for every two distinct vertices
x, y, wD(x) ?= wD(y), where wD(x) =
P
z?ND(x) g(z) and ND(x) = {z|d(x, z) ?
D}.
In this thesis, several classes of D-antimagic graphs will be discussed. |
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