| 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. | | 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. |
− | 以一个图为例{{nowrap|1=''G'' = (''V'', ''E'', ''ϕ'')}} 。'''有限步道 finite walk'''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>)}} 是移动的顶点序列。如果 {{nowrap begin}}''v''<sub>1</sub> = ''v''<sub>''n''</sub>{{nowrap end}} ,则此步道封闭,反之则开放。'''无限步道 infinite walk'''是由一系列边组成的,它们的类型与这里描述的相同,但没有起点或终点,而一个半无限步道(或光线)则有起点但是没有终点。 | + | :以一个图为例 ''G'' = (''V'', ''E'', ''ϕ'') 。'''有限步道 finite walk'''是一系列的边 (''e''<sub>1</sub>, ''e''<sub>2</sub>, …, ''e''<sub>''n'' − 1</sub>),其顶点序列(''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>) 。 ''ϕ''(''e''<sub>''i''</sub>) = {''v''<sub>''i''</sub>, ''v''<sub>''i'' + 1</sub>}对于''i'' = 1, 2, …, ''n'' − 1 . (''v''<sub>1</sub>, ''v''<sub>2</sub>, …, ''v''<sub>''n''</sub>) 是移动的顶点序列。如果 ''v''<sub>1</sub> = ''v''<sub>''n''</sub> ,则此步道封闭,反之则开放。'''无限步道 infinite walk'''是由一系列边组成的,它们的类型与这里描述的相同,但没有起点或终点,而一个半无限步道(或光线)则有起点但是没有终点。 |