This is discrete mathematics The notation Cn refers to a cyc

This is discrete mathematics

The notation C_n refers to a cycle graph with n vertices.

The chromatic number of C_{23 is _________}

The clique number of C_{23 is _________}

The size of the largest possible independent set in C₂₃ is _________

Solution

The number of maximal independent sets in n-vertex cycle graphs is given by the Perrin numbers.

In mathematics, the Perrin numbers are defined by the recurrence relation

P(n) = P(n 2) + P(n 3) for n > 2,

with initial values

P(0) = 3, P(1) = 0, P(2) = 2.

SEQUENCE IS 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, 51, 68, 90, 119, 158, 209, 277, 367, 486.

P(23) =P(21)+P(20)

WE GET P(23)=486