EconPapers    
Economics at your fingertips  
 

Paired-domination number of claw-free odd-regular graphs

Wei Yang, Xinhui An and Baoyindureng Wu ()
Additional contact information
Wei Yang: Xinjiang University
Xinhui An: Xinjiang University
Baoyindureng Wu: Xinjiang University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 4, No 6, 1266-1275

Abstract: Abstract A paired-dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching, while the paired-domination number is the minimum cardinality of a paired-dominating set in the graph, denoted by $$\gamma _{pr}(G)$$ γ p r ( G ) . Let G be a connected $$\{K_{1,3}, K_{4}-e\}$$ { K 1 , 3 , K 4 - e } -free cubic graph of order n. We show that $$\gamma _{pr}(G)\le \frac{10n+6}{27}$$ γ p r ( G ) ≤ 10 n + 6 27 if G is $$C_{4}$$ C 4 -free and that $$\gamma _{pr}(G)\le \frac{n}{3}+\frac{n+6}{9(\lceil \frac{3}{4}(g_o+1)\rceil +1)}$$ γ p r ( G ) ≤ n 3 + n + 6 9 ( ⌈ 3 4 ( g o + 1 ) ⌉ + 1 ) if G is $$\{C_{4}, C_{6}, C_{10}, \ldots , C_{2g_o}\}$$ { C 4 , C 6 , C 10 , … , C 2 g o } -free for an odd integer $$g_o\ge 3$$ g o ≥ 3 ; the extremal graphs are characterized; we also show that if G is a 2 -connected, $$\gamma _{pr}(G) = \frac{n}{3} $$ γ p r ( G ) = n 3 . Furthermore, if G is a connected $$(2k+1)$$ ( 2 k + 1 ) -regular $$\{K_{1,3}, K_4-e\}$$ { K 1 , 3 , K 4 - e } -free graph of order n, then $$\gamma _{pr}(G)\le \frac{n}{k+1} $$ γ p r ( G ) ≤ n k + 1 , with equality if and only if $$G=L(F)$$ G = L ( F ) , where $$F\cong K_{1, 2k+2}$$ F ≅ K 1 , 2 k + 2 , or k is even and $$F\cong K_{k+1,k+2}$$ F ≅ K k + 1 , k + 2 .

Keywords: Claw-free graphs; Cubic graphs; Domination; Paired-domination number; Regular graphs (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-016-0033-9 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:33:y:2017:i:4:d:10.1007_s10878-016-0033-9

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

DOI: 10.1007/s10878-016-0033-9

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:33:y:2017:i:4:d:10.1007_s10878-016-0033-9