Grinberg-Introduction-Graph-Theory · Problem 4.7

Digraphs and multidigraphs

Mathematics — Graph Theory · adjacency-matrix-walks

Problem

Let

E

be the following multidigraph:

E = \bigoplus 2 \underset{}{\longleftrightarrow} \overset{1}{\nearrow\swarrow} \underset{}{\longleftrightarrow} 3\circlearrowleft

(a multidigraph with vertices

1, 2, 3

and arcs going between them as shown in the figure on page 124). Let

k \in \mathbb{N}

. Compute the number of walks from

1

1

having length

k