Local Antimagic Vertex Coloring of a Graph
Let G = ( V , E ) be a connected graph with V = n and E = m . A bijection f : E → { 1 , 2 , ⋯ , m } is called a local antimagic labeling if for any two adjacent vertices u and v , w ( u ) ≠ w ( v ) , where w ( u ) = ∑ e ∈ E ( u ) f ( e ) , and E ( u ) is the set of edges incident to u . Thus any lo...
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| Published in | Graphs and combinatorics Vol. 33; no. 2; pp. 275 - 285 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Tokyo
Springer Japan
01.03.2017
|
| Subjects | |
| Online Access | Get full text |
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| Summary: | Let
G
=
(
V
,
E
)
be a connected graph with
V
=
n
and
E
=
m
.
A bijection
f
:
E
→
{
1
,
2
,
⋯
,
m
}
is called a local antimagic labeling if for any two adjacent vertices
u
and
v
,
w
(
u
)
≠
w
(
v
)
,
where
w
(
u
)
=
∑
e
∈
E
(
u
)
f
(
e
)
,
and
E
(
u
) is the set of edges incident to
u
. Thus any local antimagic labeling induces a proper vertex coloring of
G
where the vertex
v
is assigned the color
w
(
v
). The local antimagic chromatic number
χ
l
a
(
G
)
is the minimum number of colors taken over all colorings induced by local antimagic labelings of
G
. In this paper we present several basic results on this new parameter. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0911-0119 1435-5914 |
| DOI: | 10.1007/s00373-017-1758-7 |