Neighbor sum distinguishing total coloring of graphs embedded in surfaces of nonnegative Euler characteristic

Renyu Xu, Jianliang Wu () and Jin Xu
Additional contact information
Renyu Xu: Shandong University
Jianliang Wu: Shandong University
Jin Xu: Shandong University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 4, No 6, 1430-1442

Abstract: Abstract A total coloring of a graph $$G$$ G is a coloring of its vertices and edges such that adjacent or incident vertices and edges are not colored with the same color. A total $$[k]$$ [ k ] -coloring of a graph $$G$$ G is a total coloring of $$G$$ G by using the color set $$[k]=\{1,2,\ldots ,k\}$$ [ k ] = { 1 , 2 , … , k } . Let $$f(v)$$ f ( v ) denote the sum of the colors of a vertex $$v$$ v and the colors of all incident edges of $$v$$ v . A total $$[k]$$ [ k ] -neighbor sum distinguishing-coloring of $$G$$ G is a total $$[k]$$ [ k ] -coloring of $$G$$ G such that for each edge $$uv\in E(G)$$ u v ∈ E ( G ) , $$f(u)\ne f(v)$$ f ( u ) ≠ f ( v ) . Let $$G$$ G be a graph which can be embedded in a surface of nonnegative Euler characteristic. In this paper, it is proved that the total neighbor sum distinguishing chromatic number of $$G$$ G is $$\Delta (G)+2$$ Δ ( G ) + 2 if $$\Delta (G)\ge 14$$ Δ ( G ) ≥ 14 , where $$\Delta (G)$$ Δ ( G ) is the maximum degree of $$G$$ G .

Keywords: Neighbor sum distinguishing total coloring; Euler characteristic; Surface; 05C15 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-015-9832-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:31:y:2016:i:4:d:10.1007_s10878-015-9832-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-015-9832-7

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().