Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 2 (2016), 317-332.

Radio number for fourth power paths

Min-Lin Lo and Linda Victoria Alegria

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Let G be a connected graph. For any two vertices u and v, let d(u,v) denote the distance between u and v in G. The maximum distance between any pair of vertices of G is called the diameter of G and denoted by diam(G). A radio labeling (or multilevel distance labeling) of G is a function f that assigns to each vertex a label from the set {0,1,2,} such that the following holds for any vertices u and v: |f(u) f(v)| diam(G) d(u,v) + 1. The span of f is defined as maxu,vV (G){|f(u) f(v)|}. The radio number of G is the minimum span over all radio labelings of G. The fourth power of G is a graph constructed from G by adding edges between vertices of distance four or less apart in G. In this paper, we completely determine the radio number for the fourth power of any path, except when its order is congruent to 1(mod8).

Article information

Involve, Volume 9, Number 2 (2016), 317-332.

Received: 24 November 2014
Revised: 12 April 2015
Accepted: 12 April 2015
First available in Project Euclid: 22 November 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C78: Graph labelling (graceful graphs, bandwidth, etc.)

channel assignment problem multilevel distance labeling radio number radio labeling


Lo, Min-Lin; Alegria, Linda Victoria. Radio number for fourth power paths. Involve 9 (2016), no. 2, 317--332. doi:10.2140/involve.2016.9.317.

Export citation


  • G. Chartrand, D. Erwin, and P. Zhang, “A graph labeling problem suggested by FM channel restrictions”, Bull. Inst. Combin. Appl. 43 (2005), 43–57.
  • G. Chartrand, D. Erwin, F. Harary, and P. Zhang, “Radio labelings of graphs”, Bull. Inst. Combin. Appl. 33 (2001), 77–85.
  • W. K. Hale, “Frequency assignment: theory and applications”, Proc. IEEE 68:12 (1980), 1497–1514.
  • D. D.-F. Liu, “Radio number for trees”, Discrete Math. 308:7 (2008), 1153–1164.
  • D. D.-F. Liu and M. Xie, “Radio number for square of cycles”, Congr. Numer. 169 (2004), 101–125.
  • D. D.-F. Liu and M. Xie, “Radio number for square paths”, Ars Combin. 90 (2009), 307–319.
  • D. D.-F. Liu and X. Zhu, “Multilevel distance labelings for paths and cycles”, SIAM J. Discrete Math. 19:3 (2005), 610–621.
  • M.-L. Lo, “Radio number for cube paths”, unpublished manuscript, 2010.
  • B. Sooryanarayana, M. Vishu Kumar, and K. Manjula, “Radio number of cube of a path”, Int. J. Math. Comb. 1 (2010), 5–29.
  • P. Zhang, “Radio labelings of cycles”, Ars Combin. 65 (2002), 21–32.