Involve: A Journal of Mathematics
- Volume 9, Number 2 (2016), 317-332.
Radio number for fourth power paths
Let be a connected graph. For any two vertices and , let denote the distance between and in . The maximum distance between any pair of vertices of is called the diameter of and denoted by . A radio labeling (or multilevel distance labeling) of is a function that assigns to each vertex a label from the set such that the following holds for any vertices and : . The span of is defined as . The radio number of is the minimum span over all radio labelings of . The fourth power of is a graph constructed from by adding edges between vertices of distance four or less apart in . In this paper, we completely determine the radio number for the fourth power of any path, except when its order is congruent to .
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.)
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. https://projecteuclid.org/euclid.involve/1511371003