MathDB

[*] Let

G

be a

(4, 4)

unoriented graph, 2-regulate, containing a cycle with the length 3. Find the characteristic polynomial

P_G (\lambda)

, its spectrum

Spec (G)

and draw the graph

G

. [*] Let

G'

be another 2-regulate graph, having its characteristic polynomial

P_{G'} (\lambda) = \lambda^4 - 4\lambda^2 + \alpha, \alpha \in \mathbb{R}

. Find the spectrum

Spec(G')

and draw the graph

G'

. [*] Are the graphs

G

and

G'

cospectral or isomorphic?

W. 20