Introduction to Graph Theory · Problem 4.7

Digraphs and multidigraphs — Darij Grinberg

Mathematics — Graph Theory · adjacency-matrix-walk-counting

Problem

Let

E

be the following multidigraph:

E = \text{(a multidigraph with vertices } 1, 2, 3 \text{ with arcs: a loop at 2, two arcs from 2 to 1, one arc from 1 to 2, one arc from 2 to 3, and a loop at 3)}

Let

k \in \mathbb{N}

. Compute the number of walks from

1

1

having length

k