Simple Graph/Examples/Arbitrary Order 5

Example of Simple Graph

Let $G = \struct {V, E}$ be a simple graph such that:

$V = \set {v_1, v_2, v_3, v_4, v_5}$

$E = \set {v_1 v_2, v_1 v_4, v_1 v_5, v_2 v_3, v_3 v_5, v_4 v_5}$

Then $G$ can be presented in diagram form as:

The underlying relation $\RR$ on $V$ which defines the edge set of $G$ is:

$\RR = \set {\tuple {v_1, v_2}, \tuple {v_2, v_1}, \tuple {v_1, v_4}, \tuple {v_4, v_1}, \tuple {v_1, v_5}, \tuple {v_5, v_1}, \tuple {v_2, v_3}, \tuple {v_3, v_2}, \tuple {v_3, v_5}, \tuple {v_5, v_3}, \tuple {v_4, v_5}, \tuple {v_5, v_4} }$

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs: Problem $15$