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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

Abstract

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.

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Brianna Blake. Elizabeth Field. Jobby Jacob. "Rank numbers of graphs that are combinations of paths and cycles." Involve 6 (3) 369 - 381, 2013. https://doi.org/10.2140/involve.2013.6.369

Information

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

Subjects:
Primary: 05C15 , 05C78
Secondary: 05C38

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

Rights: Copyright © 2013 Mathematical Sciences Publishers

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