Radio Colouring of Some Graphs | Chapter 7 | Mathematics and Computer Science: Research Updates Vol. 2

Radio colouring is a mathematical model of networks. The solution of frequency assignment problem can be analyzed by radio colouring. Radio colouring was defined by Kalfakakou et al. (2003) in 2003 and an approximation algorithm has been discussed. A radio colouring is defined as colouring the vertices of G with positive integers in order that the distance two vertices are assigned different colours and adjacent vertices are coloured with difference at least two. A radio colouring that make use of k-colours is a k-radio colouring. The minimum number of colours used is the radio chromatic number rn(G). In this chapter the radio number of some acyclic graphs like path, comb, caterpillar and star graphs are analyzed. Also it has been discussed for some cyclic graphs like cycle and sunlet graph in second section.

 

Author (s) Details

 

A. Vimala Rani
Department of Mathematics, AMET University, Tamil Nadu, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v2/4012

The Study of Distance-Labelings for Cycle Graphs | Chapter 13 | Research Highlights in Mathematics and Computer Science Vol. 9

 

Let G = (V,E) be a diagram and Cm be the cycle diagram with m top. In this chapter, we persisted Yeh's work [1] on the distance labeling of the phase diagram Cm. An n-set distance labeling of a diagram G is the labeling of the top (with n labels per top) of G under certain restraints determined by the distance 'tween each pair of vertices in G. Following Yeh's documentation [1], the smallest advantage for the best label in an n-set distance labeling of G is meant by A1(n) (G)…..

Author(s) Details:

Alissa Shen,
St. Stephen’s Episcopal School, Austin, Texas, USA.

Jian Shen,
Department of Mathematics, Texas State University, San Marcos, Texas, USA.

Please see the link here: https://stm.bookpi.org/RHMCS-V9/article/view/10445