The b-chromatic number of power graphs of paths and cycles
Let G be a graph on the vertices n x x x ,..., , 2 1 . Its p-th power graph p G , has the same vertex set as G, with two distinct vertices of G adjacent in p G whenever there is a path of length at most p between them in G. The b-chromatic number of G, denoted by ) (G , is defined as the maximum num...
Saved in:
| Main Author: | |
|---|---|
| Format: | text |
| Language: | English |
| Published: |
Animo Repository
2005
|
| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_masteral/3289 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | De La Salle University |
| Language: | English |
| Summary: | Let G be a graph on the vertices n x x x ,..., , 2 1 . Its p-th power graph p G , has the same vertex set as G, with two distinct vertices of G adjacent in p G whenever there is a path of length at most p between them in G. The b-chromatic number of G, denoted by ) (G , is defined as the maximum number k of colors that can be used to color the vertices of G, such that no two adjacent vertices have the same color and for each color i, with k i 1 , there exists a vertex x of color i adjacent to a vertex of every color j, where k i j 1 . This paper discussed the b-chromatic number of the power graphs of paths and cycles. This paper is an exposition of the article entitled The b-chromatic number of some power graph by Brice Effantin and Hemamache Kheddouci which appeared in Discrete Mathematics and Theoretical Computer Science Volume 6 in 2003. This study gives the exact value for the b-chromatic number of power graphs of path. It also give the exact value for the b-chromatic number of p n C when ] 3 , 3 2 [ p p n + and a bound for the b-chromatic number of p n C when ] 3 , 3 2 [ p p n + . |
|---|