Degree conditions for weakly geodesic pancyclic graphs and their exceptions

Emlee W. Nicholson () and Bing Wei ()
Additional contact information
Emlee W. Nicholson: Millsaps College
Bing Wei: University of Mississippi

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 30, 912-917

Abstract: Abstract Let $$G$$ G be a graph on $$n$$ n vertices. Let $$\sigma _2(G)=\text {min}\{d_G(u)+d_G(v):u,v\in {V(G)};uv\notin {E(G)}\}$$ σ 2 ( G ) = min { d G ( u ) + d G ( v ) : u , v ∈ V ( G ) ; u v ∉ E ( G ) } when $$G$$ G is not complete, otherwise set $$\sigma _2(G)=\infty $$ σ 2 ( G ) = ∞ . A graph $$G$$ G is said to be weakly geodesic pancyclic if for each pair of vertices $$u,v\in {V(G)}$$ u , v ∈ V ( G ) , every shortest $$u,v$$ u , v -path lies on a cycle of length $$k$$ k where $$k$$ k is an integer between the length of a shortest cycle containing the $$u,v$$ u , v -path and $$n$$ n . In this paper, we will show that if $$\sigma _2(G)\ge {n+1}$$ σ 2 ( G ) ≥ n + 1 then $$G$$ G is either weakly geodesic pancyclic or belongs to one of four exceptional classes of graphs, which are completely determined. Our results generalize some recent results of Chan et al. (Discret Appl Math 155:1971-1978, 2007).

Keywords: Pancyclic; Geodesic; Exceptional classes (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-014-9800-7 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:2:d:10.1007_s10878-014-9800-7

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

DOI: 10.1007/s10878-014-9800-7

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 ().