EconPapers    
Economics at your fingertips  
 

Neighbor sum distinguishing total coloring of 2-degenerate graphs

Jingjing Yao, Xiaowei Yu, Guanghui Wang and Changqing Xu ()
Additional contact information
Jingjing Yao: Hebei University of Technology
Xiaowei Yu: Shandong University
Guanghui Wang: Shandong University
Changqing Xu: Hebei University of Technology

Journal of Combinatorial Optimization, 2017, vol. 34, issue 1, No 4, 64-70

Abstract: Abstract A proper k-total coloring of a graph G is a mapping from $$V(G)\cup E(G)$$ V ( G ) ∪ E ( G ) to $$\{1,2,\ldots ,k\}$$ { 1 , 2 , … , k } such that no two adjacent or incident elements in $$V(G)\cup E(G)$$ V ( G ) ∪ E ( G ) receive the same color. Let f(v) denote the sum of the colors on the edges incident with v and the color on vertex v. A proper k-total coloring of G is called neighbor sum distinguishing if $$f(u)\ne f(v)$$ f ( u ) ≠ f ( v ) for each edge $$uv\in E(G)$$ u v ∈ E ( G ) . Let $$\chi ''_{\Sigma }(G)$$ χ Σ ′ ′ ( G ) denote the smallest integer k in such a coloring of G. Pilśniak and Woźniak conjectured that for any graph G, $$\chi ''_{\Sigma }(G)\le \Delta (G)+3$$ χ Σ ′ ′ ( G ) ≤ Δ ( G ) + 3 . In this paper, we show that if G is a 2-degenerate graph, then $$\chi ''_{\Sigma }(G)\le \Delta (G)+3$$ χ Σ ′ ′ ( G ) ≤ Δ ( G ) + 3 ; Moreover, if $$\Delta (G)\ge 5$$ Δ ( G ) ≥ 5 then $$\chi ''_{\Sigma }(G)\le \Delta (G)+2$$ χ Σ ′ ′ ( G ) ≤ Δ ( G ) + 2 .

Keywords: Neighbor sum distinguishing total coloring; 2-Degenerate graph; Combinatorial Nullstellensatz; Lexicographic order (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-016-0053-5 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:34:y:2017:i:1:d:10.1007_s10878-016-0053-5

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

DOI: 10.1007/s10878-016-0053-5

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 ().

 
Page updated 2025-03-20
Handle: RePEc:spr:jcomop:v:34:y:2017:i:1:d:10.1007_s10878-016-0053-5