- Tytuł:
- Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs
- Autorzy:
-
Song, Wen-Yao
Miao, Lian-Ying
Duan, Yuan-Yuan - Powiązania:
- https://bibliotekanauki.pl/articles/32083736.pdf
- Data publikacji:
- 2020-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
neighbor sum distinguishing total choosability
maximum degree
IC-planar graph
Combinatorial Nullstellensatz - Opis:
- Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph $G$ has a drawing in the plane such that every two crossings are independent, then we call $G$ a plane graph with independent crossings or IC-planar graph for short. A proper total-$k$-coloring of a graph $G$ is a mapping $ c : V (G) \cup E(G) \rightarrow \{ 1, 2, . . ., k \} $ such that any two adjacent elements in $ V (G) \cup E(G) $ receive different colors. Let $ \Sigma_c (v) $ denote the sum of the color of a vertex $v$ and the colors of all incident edges of $v$. A total-$k$-neighbor sum distinguishing-coloring of $G$ is a total-$k$-coloring of $G$ such that for each edge $ uv \in E(G)$, $\Sigma_c (u) \ne \Sigma_c (v) $. The least number $k$ needed for such a coloring of $G$ is the neighbor sum distinguishing total chromatic number, denoted by $ \chi_\Sigma^{''} (G) $. In this paper, it is proved that if $G$ is an IC-planar graph with maximum degree $ \Delta (G) $, then $ ch_\Sigma^{''} (G) \le \text{max} \{ \Delta (G)+3, 17 \} $, where $ ch_\Sigma^{''} (G) $ is the neighbor sum distinguishing total choosability of $G$.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 331-344
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł