Degree of Vertex/Examples

Examples of Degrees of Vertices

The degrees of the vertices of the above graph are:

$\ds \map \deg {v_1}$

$=$

$\ds 2$

$\ds \map \deg {v_2}$

$=$

$\ds 2$

$\ds \map \deg {v_3}$

$=$

$\ds 3$

$\ds \map \deg {v_4}$

$=$

$\ds 1$

$\ds \map \deg {v_5}$

$=$

$\ds 0$

There exists no simple graph whose vertices have degrees $1, 3, 3, 3$.

You arrive at a small party with your partner, which $3$ other couples are also attending.

Several handshakes took place.

Nobody shook hands with themselves or their partners.

Nobody shook hands with anyone else more than once.

After all the handshaking had taken place, you asked each person, including your partner, how many times they had shaken hands.

Every person replied with a different answer.

$(1): \quad$ How many times did you shake hands?

$(2): \quad$ How many times did your partner shake hands?