On Chromaticity of Wheels

Let the vertices of a graph such that every two
adjacent vertices have different color is a very common problem in
the graph theory. This is known as proper coloring of graphs. The
possible number of different proper colorings on a graph with a given
number of colors can be represented by a function called the
chromatic polynomial. Two graphs G and H are said to be
chromatically equivalent, if they share the same chromatic
polynomial. A Graph G is chromatically unique, if G is isomorphic to
H for any graph H such that G is chromatically equivalent to H. The
study of chromatically equivalent and chromatically unique problems
is called chromaticity. This paper shows that a wheel W12 is
chromatically unique.

• Zainab Yasir Al-Rekaby
• Abdul Jalil M. Khalaf

• Chromatic Polynomial
• Chromatically Equivalent
• Chromatically Unique
• Wheel.

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