## Involve: A Journal of Mathematics

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

### Radio number for fourth power paths

#### Abstract

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 $maxu,v∈V (G){|f(u) − f(v)|}$. 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

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

Dates
Revised: 12 April 2015
Accepted: 12 April 2015
First available in Project Euclid: 22 November 2017

https://projecteuclid.org/euclid.involve/1511371003

Digital Object Identifier
doi:10.2140/involve.2016.9.317

Mathematical Reviews number (MathSciNet)
MR3470734

Zentralblatt MATH identifier
1333.05266

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

#### Citation

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

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