Graph Teory (23/08/2024)

Consider an adjacency matrix $A$, such that

$A_{ij}=1\text{ if there is an edge from vertex }j\text{ to vertex }i,$

$A_{ij} = 1 \text{ if there is an edge from vertex } j \text{ to vertex }$$A_{ij}=0\text{ otherwise}\mathrm{.}$

Select the correct alternative:

a) If the graph is undirected, $A = A^T$.

b) If the graph is directed, the main diagonal is always equal to 1.

c) If the graph is undirected, the main diagonal is always equal to 0.

d) If the graph is directed, $A$ is invertible.

e) None of the above

Original idea by: João Vitor Baptista Moreira