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The b-Chromatic Index of a Graph.
- Source :
- Bulletin of the Malaysian Mathematical Sciences Society; Oct2015, Vol. 38 Issue 4, p1375-1392, 18p, 8 Diagrams
- Publication Year :
- 2015
-
Abstract
- The b-chromatic index $$\varphi '(G)$$ of a graph $$G$$ is the largest integer $$k$$ such that $$G$$ admits a proper $$k$$ -edge coloring in which every color class contains at least one edge incident to some edge in all the other color classes. The b-chromatic index of trees is determined and equals either to a natural upper bound $$m'(T)$$ or one less, where $$m'(T)$$ is connected with the number of edges of high degree. Some conditions are given for which graphs have the b-chromatic index strictly less than $$m'(G)$$ , and for which conditions it is exactly $$m'(G)$$ . In the last part of the paper, regular graphs are considered. It is proved that with four exceptions, the b-chromatic index of cubic graphs is $$5$$ . The exceptions are $$K_4$$ , $$K_{3,3}$$ , the prism over $$K_3$$ , and the cube $$Q_3$$ . [ABSTRACT FROM AUTHOR]
- Subjects :
- GRAPHIC methods
CHROMATICITY
FIXED point theory
ALGORITHMS
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 01266705
- Volume :
- 38
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Bulletin of the Malaysian Mathematical Sciences Society
- Publication Type :
- Academic Journal
- Accession number :
- 109251151
- Full Text :
- https://doi.org/10.1007/s40840-014-0088-7