 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/17j/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

(A^{r})_{ij}

counts length-

r

walks from

i

j

, so

tr A^{r}

counts length-

r

closed walks. The given power sums identify the spectrum as

5

once,

5

and

- 5

three times each, and

- 1

five times. Thus

n = 12

, regular degree

d = 5

, and the size is

n d /2 = 30

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