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

Study on Neighborhood Prime Labeling | Chapter 7 | Current Topics on Mathematics and Computer Science Vol. 5

A labelling or numbering of a graph G is the assignment of labels to the graph's vertices, which results in a labelling for each edge uv based on the vertex labels f(u) and f(f) (v). Neighborhood prime labelling of Star graphs, Complete bipartite graphs, Fan graphs, Friendship graphs, Flower graphs, Bistar graphs, Comb graphs, Pn splitting graphs, and K1,n splitting graphs are covered in this work. Also covered are the neighbourhood prime labelling in the Ring sum of cycles Cn and K1,n, as well as various graph operations on the Fan and Friendship graphs.

Author (s) Details

Dr.  T. J. Rajesh Kumar
Department of Mathematics, TKM College of Engineering, Kollam, Kerala, India.

View Book :- https://stm.bookpi.org/CTMCS-V5/article/view/2434