# Terminology - exercises ¶

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These are easy questions, to make sure that you understood and remembered the vocabulary. We will use this graph $G(V, E)$ for the following questions

• give $V$ (the set of vertices)

$V=\text{ {a,b,c,d,e,f,g,h,i} }$

• give $E$ (the set of edges)

$E=\text{ {(a,b),(a,d),(b,a),(b,d),(b,h),(c,a),(d,h),(d,c), (h,i),(i,h),(e,f),(e,g),(c,i)} }$

• give $\Gamma(a)$, $\Gamma(b)$, $\Gamma(c)$

The number of neighbors of

• a is $\Gamma(a) = \Gamma(a)^+ + \Gamma(a)^- = 2 + 2 = 4$
• b is $\Gamma(b) = \Gamma(b)^+ + \Gamma(b)^- = 1 + 3 = 4$
• c is $\Gamma(c) = \Gamma(c)^+ + \Gamma(c)^- = 2 + 1 = 3$

• give a path, a cycle, a chain, and a circuit
• path: a,b
• cycle: a,b
• chain: a,b,h,i
• circuit: a,d,c