The main problem in vertex coloring is how to color each vertex on a graph so that no two adjacent
vertices have the same color. Fractional coloring is a double coloring at vertices of different colors where the
adjacent vertices have different colors. In operations on the graph, one of them is known as amalgamation operation.
Amalgamation in the graph is divided into two, namely vertex amalgamation and side amalgamation. Coloring
vertex can be applied to the graph which is the result of the operation of some special graphs. Amalgamation
operation is to combine the vertices or sides of each graph to form a new graph. In this case, the resulting
amalgamation graph will produce the same fractional chromatic number with one of the fractional chromatic figures
of the graph prior to be amalgamated.

Published In:IJCSN Journal Volume 7, Issue 3

Date of Publication : June 2018

Pages : 158-165

Figures :--

Tables : 01

Junianto Sesa : Department of Mathematics, University of Hasanuddin, Makassar, South Sulawesi, Indonesia.

Armin Lawi : Department of Mathematics, University of Hasanuddin, Makassar, South Sulawesi, Indonesia.

Hasmawati : Department of Mathematics, University of Hasanuddin, Makassar, South Sulawesi, Indonesia.

Siswanto : Department of Statistics, Bogor Agricultural University, Bogor, West Java, Indonesia.

From the description or explanation above, the
researchers can conclude that fractional chromatic
numbers are very useful in the world of technology,
especially in the field of index code. The fractional
chromatic number of some graphs when combined
using an amalgamation operation will result in the
same as one chromatic fractional graph before the
operation.

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