Open Access
Translator Disclaimer
2013 Rank numbers of graphs that are combinations of paths and cycles
Brianna Blake, Elizabeth Field, Jobby Jacob
Involve 6(3): 369-381 (2013). DOI: 10.2140/involve.2013.6.369


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 u-v path contains a vertex w such that f(w)>f(u). The rank number of G, denoted χr(G), is the minimum k such that a k-ranking exists for G. It is shown that given a graph G and a positive integer t, the question of whether χr(G)t is NP-complete. However, the rank number of numerous families of graphs have been established. We study and establish rank numbers of some more families of graphs that are combinations of paths and cycles.


Download Citation

Brianna Blake. Elizabeth Field. Jobby Jacob. "Rank numbers of graphs that are combinations of paths and cycles." Involve 6 (3) 369 - 381, 2013.


Received: 25 April 2013; Accepted: 29 July 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1274.05143
MathSciNet: MR3101767
Digital Object Identifier: 10.2140/involve.2013.6.369

Primary: 05C15 , 05C78
Secondary: 05C38

Keywords: $k$-ranking , cycles , Paths , rank number , ranking

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.6 • No. 3 • 2013
Back to Top