西北师范大学数学与统计学院,甘肃 兰州 730070
马静静(1997年生),女;研究方向:图论及其应用;E-mail:majingjing0213@163.com
陈祥恩(1965年生),男;研究方向:图论及其应用;E-mail:chenxe@nwnu.edu.cn
纸质出版日期:2020-07-20,
收稿日期:2019-06-12,
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马静静,陈祥恩.K4,4,p的点可区别的IE-全染色(4≤ p ≤1 007)[J].中山大学学报(自然科学版),2020,59(04):134-143.
MA Jingjing,CHEN Xiang'en.Vertex-distinguishing IE-total coloring of K4,4,p (4≤ p ≤1 007)[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(04):134-143.
马静静,陈祥恩.K4,4,p的点可区别的IE-全染色(4≤ p ≤1 007)[J].中山大学学报(自然科学版),2020,59(04):134-143. DOI: 10.13471/j.cnki.acta.snus.2019.06.12.2019A047.
MA Jingjing,CHEN Xiang'en.Vertex-distinguishing IE-total coloring of K4,4,p (4≤ p ≤1 007)[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(04):134-143. DOI: 10.13471/j.cnki.acta.snus.2019.06.12.2019A047.
图
G
的IE-全染色
f
是指使得图
G
的任意两个相邻的顶点的颜色不同的一个一般全染色。设
f
是图
G
的IE-全染色,若对图
G
的任意两个不同的顶点
u
,
v
,有
C
(
u
)≠
C
(
v
),其中
C
f
(
x
)
或
C
(
x
)表示
f
为下点
x
的颜色及与
x
关联的边的颜色所构成的集合,则
f
称为图
G
的点可区别IE-全染色(简记为VDIETC)。利用色集事先分配法,构造染色法,反证法探讨了完全三部图
K
4
4
p
(4≤
p
≤1 007)的点可区别IE-全染色问题,确定了
K
4
4
p
(4≤
p
≤1 007)的点可区别IE-全染色数。
Let
G
be a simple graph.An IE-total coloring
<math id="M1"><mi>f</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49498994&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49498975&type=
1.10066664
3.47133350
of
G
is called that if there are no two adjacent vertices of
G
receive the same color
For an IE-total coloring
f
of
G
if
C
(
u
)≠
C
(
v
) for two distinct vertex
u
and
v
where
C
f
(
x
)
or
C
(
x
) denotes the set of colors of vertex
x
and of the edges incident with
x
under
f
then
f
is called a vertex-distingushing IE-total coloring of
G
.By using of themethods of distributing the color sets in advance
constructing the colorings and contradiction
the vertex-distinguishing IE-total coloring of complete tripartite graphs
K
4
4
p
(4≤
p
≤1 007) is discussed.The vertex-distinguishing IE-total chromatic number of
K
4
4
p
(4≤
p
≤1 007) is determined.
完全三部图IE-全染色点可区别IE-全染色
complete tripartite graphIE-total coloringvertex-distinguishing IE-total coloring
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