Question

The graph G shown below is the union of three connected components G1,G2,G3.(The graph G consists of the three connected components G1, G2 and G3.)

(1)what is Chromatic numberχ(G)

(2)what is Chromatic polynomialρG(k) (do not expand).

(3)what is the number of 6-colorings of G. (No need to simplify the answer.)

Gi G2 G3

Answer 1

1. the chromatic number of a graph is the minimum no. of colors requered in a proper coloring. Here X(G) = 5 a, b, c, d, e are different to los b d C b e 59 G

the Of 2. Chromatic polynomial of a disconnected graph er is produd of the chromatic polynomial components. il, PG (A) = P(A). Per (A). Pogle) Puld = (2-1)... Ca-nto) Por, LA) = X (A-,)..(-5) Per, (x) = h (dos)..(d-by) P G₂ (4) = (dos)..(-3) i. PG (4) = x (h. 13. (1-3)= (1-4) (0-5) 3 since G contains 6 vertices, can put different Then to colors each vexlex. we get 6- coloring. a 5 different Colors to each again gel another Again giving vertex 6- coloring dind 2. 6-colorings We can smus

Thank you so much sir