rosen graph theory

Question

find the values (k tuple coloring )

1)$X_{2}(K_{3}) 2. X_{3}(K_{5})$

Answer 1

k- tuple coloring of a graph G is an assignment of a set of k different colors to each of the vertices of G such that no two adjacent vertices are assigned a common color.We de-note by χk(G)the smallest positive integer n such that G has a k- tuple coloring using n colors.

1)X2(K3)

To see this, note that using only six colors we can assign two colors to each vertex of K3, so that no two adjacent vertices are assigned the same color.

same procedure u will do for next

Comments

How is this different from chromatic number? Do we need to color to assign two colors to each vertex?

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yes like that

X2(K3) :- in  K₃ graph you have to take two color for each vertex such that no two adjacent vertices are assigned the same color.

X3(K5) :- in  K₅ graph you have to take three color for each vertex such that no two adjacent vertices are assigned the same color.

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thanks  :)

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Its the value of x which tells how many colors for each vertex.Thanks.:)

Can i find the chromatic number and then multiply it with n. Will it give correct answer always?