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Let {{nowrap|1=''G'' = (''V'', ''E'', ''ϕ'')}} be a graph. A finite walk is a sequence of edges {{nowrap|(''e''<sub>1</sub>, ''e''<sub>2</sub>, …, ''e''<sub>''n'' − 1</sub>)}} for which there is a sequence of vertices {{nowrap|(''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>)}} such that {{nowrap begin}}''ϕ''(''e''<sub>''i''</sub>) = {''v''<sub>''i''</sub>, ''v''<sub>''i'' + 1</sub>}{{nowrap end}} for {{nowrap|1=''i'' = 1, 2, …, ''n'' − 1}}. {{nowrap|(''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>)}} is the ''vertex sequence'' of the walk. This walk is ''closed'' if {{nowrap begin}}''v''<sub>1</sub> = ''v''<sub>''n''</sub>{{nowrap end}}, and ''open'' else. An infinite walk is a sequence of edges of the same type described here, but with no first or last vertex, and a semi-infinite walk (or [[End (graph theory)|ray]]) has a first vertex but no last vertex.
Let {{nowrap|1=''G'' = (''V'', ''E'', ''ϕ'')}} be a graph. A finite walk is a sequence of edges {{nowrap|(''e''<sub>1</sub>, ''e''<sub>2</sub>, …, ''e''<sub>''n'' − 1</sub>)}} for which there is a sequence of vertices {{nowrap|(''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>)}} such that {{nowrap begin}}''ϕ''(''e''<sub>''i''</sub>) = {''v''<sub>''i''</sub>, ''v''<sub>''i'' + 1</sub>}{{nowrap end}} for {{nowrap|1=''i'' = 1, 2, …, ''n'' − 1}}. {{nowrap|(''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>)}} is the ''vertex sequence'' of the walk. This walk is ''closed'' if {{nowrap begin}}''v''<sub>1</sub> = ''v''<sub>''n''</sub>{{nowrap end}}, and ''open'' else. An infinite walk is a sequence of edges of the same type described here, but with no first or last vertex, and a semi-infinite walk (or [[End (graph theory)|ray]]) has a first vertex but no last vertex.
Let be a graph. A finite walk is a sequence of edges for which there is a sequence of vertices such that ϕ(e<sub>i</sub>) = {v<sub>i</sub>, v<sub>i + 1</sub>} for . is the vertex sequence of the walk. This walk is closed if v<sub>1</sub> = v<sub>n</sub>, and open else. An infinite walk is a sequence of edges of the same type described here, but with no first or last vertex, and a semi-infinite walk (or ray) has a first vertex but no last vertex.
让我们做一个图{{nowrap|1=''G'' = (''V'', ''E'', ''ϕ'')}} 。有限步道是一系列的边{{nowrap|(''e''<sub>1</sub>, ''e''<sub>2</sub>, …, ''e''<sub>''n'' − 1</sub>)}}，其顶点序列{{nowrap|(''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>)}}。 {{nowrap begin}}''ϕ''(''e''<sub>''i''</sub>) = {''v''<sub>''i''</sub>, ''v''<sub>''i'' + 1</sub>}{{nowrap end}}对于{{nowrap|1=''i'' = 1, 2, …, ''n'' − 1}}. {{nowrap|(''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>)}} 是行走的顶点序列。如果 {{nowrap begin}}''v''<sub>1</sub> = ''v''<sub>''n''</sub>{{nowrap end}} ，则此步道关闭，否则就打开。一个无限步道是一系列的边，它们的类型与这里描述的相同，但是没有第一个顶点或最后一个顶点，而一个半无限步道(或光线)有第一个顶点，但是没有最后一个顶点。
让我们做一个图{{nowrap|1=''G'' = (''V'', ''E'', ''ϕ'')}} 。有限步道是一系列的边{{nowrap|(''e''<sub>1</sub>, ''e''<sub>2</sub>, …, ''e''<sub>''n'' − 1</sub>)}}，其顶点序列{{nowrap|(''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>)}}。 {{nowrap begin}}''ϕ''(''e''<sub>''i''</sub>) = {''v''<sub>''i''</sub>, ''v''<sub>''i'' + 1</sub>}{{nowrap end}}对于{{nowrap|1=''i'' = 1, 2, …, ''n'' − 1}}. {{nowrap|(''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>)}} 是行走的顶点序列。如果 {{nowrap begin}}''v''<sub>1</sub> = ''v''<sub>''n''</sub>{{nowrap end}} ，则此步道关闭，否则就打开。一个无限步道是一系列的边，它们的类型与这里描述的相同，但是没有第一个顶点或最后一个顶点，而一个半无限步道(或光线)有第一个顶点，但是没有最后一个顶点。