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Математические заметки, 2022, том 112, выпуск 1, статья опубликована в англоязычной версии журнала
(Mi mzm13348)
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Статьи, опубликованные в английской версии журнала
On the
$D(2)$-Vertex Distinguishing Total Coloring
of Graphs with
$\Delta=3$
Fei Wena, Xiuqing Jiaa, Zepeng Lib, Muchun Lia a Institute of Applied Mathematics, Lanzhou Jiaotong
University, Lanzhou, 730070 China
b School of Information Science and Engineering, Lanzhou
University, Lanzhou, 730000 China
Аннотация:
A $D(2)$-vertex-distinguishing total coloring of a graph
$G$
is a proper total
coloring such that no pair of vertices, within distance two, has the same set of colors,
and the minimum number of colors required for such a coloring is called
$D(2)$-vertex-distinguishing total chromatic number of
$G$,
and denoted by
$\chi_{2vt}(G)$.
In this paper, we prove that
$\chi_{2vt}(G)\leq11$
for any graph
$G$
with
$\Delta(G)=3$.
Ключевые слова:
total coloring,
$D(2)$-vertex-distinguishing total coloring,
$D(2)$-vertex-distinguishing
total chromatic number.
Поступило: 05.11.2021 Исправленный вариант: 20.12.2021
Образец цитирования:
Fei Wen, Xiuqing Jia, Zepeng Li, Muchun Li, “On the
$D(2)$-Vertex Distinguishing Total Coloring
of Graphs with
$\Delta=3$”, Math. Notes, 112:1 (2022), 142–149
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/mzm13348
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