Rank numbers of graphs that are combinations of paths and cycles

Blake, Brianna; Field, Elizabeth H.; Jacob, Jobby

doi:10.2140/involve.2013.6.369

Search citation statements

Order By: Relevance

Paper Sections

Select...

Results1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also characterized subdivided stars based on their rank numbers, thus establishing the rank number of all subdivided stars. Rankings of some other classes of trees have also been studied by others, for example see [7,10,14], however, the rank number of an arbitrary tree has not been established.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Graphs with large rank numbers and rank numbers of subdivided stars

Boynton

Burroughs

Gaston

et al. 2020

AKCE International Journal of Graphs and Combinatorics

Self Cite

View full text Add to dashboard Cite

A k-ranking of a graph G is a function f : V (G) → {1, 2,. .. , k} such that if f (u) = f (v) then every uv path contains a vertex w such that f (w) > f (u). The rank number of G, denoted χ r (G), is the minimum k such that a k-ranking exists for G. It is known that given a graph G and a positive integer t the question of whether χ r (G) ≤ t is NP-complete. In this paper we characterize graphs with large rank numbers. In addition, we characterize subdivided stars based on their rank numbers.

show abstract

Section: Resultsmentioning

confidence: 99%

“…The mathematical studies of vertex rankings were initiated by Ghoshal and Laskar in [5]. Since then, the rank number of numerous families of graphs have been established, for example see [6][7][8][9][10][11][12][13][14]. A generalization of k-ranking using the l p norm is discussed in [15].…”

Section: Introductionmentioning

confidence: 99%