Vertices, Edges and Weighted Graphs

Question 1

In graph theory, a point is called a

Accepted Answer

vertex — A point in a graph is a vertex; the lines joining them are edges.

Question 2

The degree of a vertex is

Accepted Answer

the number of edges meeting at it — Degree counts the edges meeting at a vertex; a loop counts as $2$.

Question 3

A graph has $6$ edges. The sum of all vertex degrees is

Accepted Answer

$12$ — Sum of degrees $=2	imes6=12$.

Question 4

An edge that carries a number such as distance or cost is found in a

Accepted Answer

weighted graph — A weighted graph labels each edge with a number (its weight).

Question 5

A loop contributes ___ to the degree of a vertex.

Accepted Answer

$2$ — A loop meets the vertex at both ends, so it adds $2$.

Question 6

A graph whose edges have arrows showing direction is called

Accepted Answer

directed — Arrows on the edges make the graph a directed graph.

Question 7

A graph has $3$ vertices with degrees $2$, $4$ and $2$. How many edges does it have?

Accepted Answer

$4$ — Edges $=\frac{2+4+2}{2}=\frac{8}{2}=4$.

Question 8

A graph has $4$ vertices and $5$ edges. Three vertices have degrees $2$, $3$, $2$. The degree of the fourth vertex is

Accepted Answer

$3$ — Total degree $=2	imes5=10$; fourth $=10-(2+3+2)=3$.

Question 9

Which statement about undirected graphs is correct?

Accepted Answer

Edges have no direction — In an undirected graph the edges have no arrows, so no direction.

Question 10

The total degree of any graph is always

Accepted Answer

even — The total degree $=2	imes(	ext{edges})$, which is always even.