Size of Graph/Examples
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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: