Size of Graph/Examples

Examples of Size of Graph

Arbitrary Order $4$ Graph

Let $G = \struct {V, E}$ be the graph defined as:

$V = \set {v_1, v_2, v_3, v_4}$.

$E = \set {\set {\tuple {v_1, v_2}, \tuple {v_2, v_1} }, \set {\tuple {v_1, v_3}, \tuple {v_3, v_1} }, \set {\tuple {v_2, v_3}, \tuple {v_3, v_2} }, \set {\tuple {v_3, v_4}, \tuple {v_4, v_3} } }$

Then the size of $G$ is the cardinality of $E$:

$\card E = 4$

Order $3$ Graphs

Let $G$ be a simple graph of order $3$.

Then it is possible for $G$ to have a size of $0$, $1$, $2$ or $3$.

Examples of each are presented below: