Neighbor sum distinguishing total choice number of IC-planar graphs with restrictive conditions
A neighbor sum distinguishing (NSD) total coloring $ \phi $ of $ G $ is a proper total coloring such that $ \sum_{z\in E_{G}(u)\cup\{u\}}\phi(z)\neq\sum_{z\in E_{G}(v)\cup\{v\}}\phi(z) $ for each edge $ uv\in E(G) $. Pilśniak and Woźniak asserted that each graph with a maximum degree $ \Delta $ admi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-04-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023692?viewType=HTML |
| Summary: | A neighbor sum distinguishing (NSD) total coloring $ \phi $ of $ G $ is a proper total coloring such that $ \sum_{z\in E_{G}(u)\cup\{u\}}\phi(z)\neq\sum_{z\in E_{G}(v)\cup\{v\}}\phi(z) $ for each edge $ uv\in E(G) $. Pilśniak and Woźniak asserted that each graph with a maximum degree $ \Delta $ admits an NSD total $ (\Delta+3) $-coloring in 2015. In this paper, we prove that the list version of this conjecture holds for any IC-planar graph with $ \Delta\geq10 $ but without five cycles by applying the discharging method, which improves the result of Zhang (NSD list total coloring of IC-planar graphs without five cycles). |
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| ISSN: | 2473-6988 |