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- Title
Coloring of a non-zero component graph associated with a finite dimensional vector space.
- Authors
Nikandish, R.; Maimani, H. R.; Khaksari, A.
- Abstract
A graph is called weakly perfect if its vertex chromatic number equals its clique number. Let be a vector space over a field with as a basis and as the null vector. The non-zero component graph of with respect to , denoted by , is a graph with the vertex set and two distinct vertices and are adjacent if and only if there exists at least one along which both and have non-zero components. In this paper, it is shown that is a weakly perfect graph. Also, we give an explicit formula for the vertex chromatic number of . Furthermore, it is proved that the edge chromatic number of is equal to the maximum degree of .
- Subjects
GRAPH theory; DIMENSIONAL analysis; VECTOR spaces; GROUP theory; POWER series
- Publication
Journal of Algebra & Its Applications, 2017, Vol 16, Issue 9, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498817501730