Handshake Lemma/Examples/Arbitrary Order 8 Graph

Examples of Use of Handshake Lemma

The above simple graph has $8$ vertices and $10$ edges (which can be ascertained by counting).

$\ds \map \deg {v_1}$

$=$

$\ds 2$

$\ds \map \deg {v_2}$

$=$

$\ds 3$

$\ds \map \deg {v_3}$

$=$

$\ds 3$

$\ds \map \deg {v_4}$

$=$

$\ds 3$

$\ds \map \deg {v_5}$

$=$

$\ds 4$

$\ds \map \deg {v_6}$

$=$

$\ds 1$

$\ds \map \deg {v_7}$

$=$

$\ds 2$

$\ds \map \deg {v_8}$

$=$

$\ds 2$

$\ds \leadsto \ \ $

$\ds \sum \map \deg V$

$=$

$\ds 2 + 3 + 3 + 3 + 4 + 1 + 2 + 2$

$\ds $

$=$

$\ds 20$

$\ds $

$=$

$\ds 2 \times 10$

1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $2$: Elementary Concepts of Graph Theory: $\S 2.1$: The Degree of a Vertex: Problem $1$