Simple Graph of Maximum Size is Complete Graph/Examples/Order 3

Examples of Use of Simple Graph of Maximum Size is Complete Graph

Let $G$ be the simple graph of order $3$ whose edge set $E$ is as large as possible.

Then the size of $G$ is given by:

$\size E = 3$

Proof

By Simple Graph of Maximum Size is Complete Graph:

$G = K_3$

From Size of Complete Graph:

$\size E = \dfrac {3 \times \paren {3 - 1} } 2 = \dfrac 6 2 = 3$

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs: Problem $18 \ \text {(a)}$