Use Figure 12.161 to determine whether the given circuit is a Hamilton cycle, an Euler circuit, both,

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Use Figure 12.161 to determine whether the given circuit is a Hamilton cycle, an Euler circuit, both, or neither.

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1. \(a \rightarrow b \rightarrow c \rightarrow e \rightarrow h \rightarrow g \rightarrow f \rightarrow d \rightarrow a\)
2. \(g \rightarrow e \rightarrow h \rightarrow g \rightarrow f \rightarrow d \rightarrow a \rightarrow b \rightarrow d \rightarrow g\)
3. \(a \rightarrow b \rightarrow c \rightarrow e \rightarrow h \rightarrow g \rightarrow f \rightarrow d \rightarrow b \rightarrow e \rightarrow g \rightarrow d \rightarrow a\)

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