Question

11. Calculate the chromatic polynomials of the following graphs: (a) $K_{1,3}$ (the complete bipartite graph with vertex partitions of cardinalities 1 and 3) (b) $K_{1,5}$ (c) $C_4$ (the cycle graph with four vertices) (d) $C_5$ (e) $K_4$ minus an edge (f) trees with $n$ vertices

          11. Calculate the chromatic polynomials of the following graphs:
(a) $K_{1,3}$ (the complete bipartite graph with vertex partitions of cardinalities 1 and 3)
(b) $K_{1,5}$
(c) $C_4$ (the cycle graph with four vertices)
(d) $C_5$
(e) $K_4$ minus an edge
(f) trees with $n$ vertices

11. Calculate the chromatic polynomials of the following graphs:
(a) K1,3 (the complete bipartite graph with vertex partitions of cardinalities 1 and 3)
(b) K1,5
(c) C4 (the cycle graph with four vertices)
(d) C5
(e) K4 minus an edge
(f) trees with n vertices

Added by Frank B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Nick Johnson

Step 1

This is because the single vertex can be colored in k ways, and each of the three vertices connected to it can be colored in (k-1) ways. (b) K1,5: Similarly, the chromatic polynomial is P(K1,5, k) = k(k-1)^5. (c) C4: The chromatic polynomial is P(C4, k) = Show more…

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11. Calculate the chromatic polynomials of the following graphs: (a) K1,3 (the complete bipartite graph with vertex partitions of cardinalities 1 and 3) (b) K1,5 (c) C4 (the cycle graph with four vertices) (d) C5 (e) K4 minus an edge (f) trees with n vertices