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*A vertex with degree 0 is called an [[isolated vertex]].
*A vertex with degree 0 is called an [[isolated vertex]].
度值为0的顶点成为'''<font color="#ff8000">孤立顶点 Isolated Vertex</font>'''
*A vertex with degree 1 is called a leaf vertex or end vertex, and the edge incident with that vertex is called a pendant edge. In the graph on the right, {3,5} is a pendant edge. This terminology is common in the study of [[tree (graph theory)|tree]]s in graph theory and especially [[tree (data structure)|tree]]s as [[data structure]]s.
*A vertex with degree 1 is called a leaf vertex or end vertex, and the edge incident with that vertex is called a pendant edge. In the graph on the right, {3,5} is a pendant edge. This terminology is common in the study of [[tree (graph theory)|tree]]s in graph theory and especially [[tree (data structure)|tree]]s as [[data structure]]s.
度值为1的顶点称为叶顶点或尾顶点，该顶点的入射边称为'''<font color="#ff8000">悬挂边 Pendant Edge</font>'''。在右侧的图中，{3,5}就是一个悬挂边。在图论中，该术语主要在研究'''<font color="#ff8000">树 Tree</font>'''时使用，特别是具有树形结构的数据。
* A vertex with degree ''n'' − 1 in a graph on ''n'' vertices is called a [[dominating vertex]].
* A vertex with degree ''n'' − 1 in a graph on ''n'' vertices is called a [[dominating vertex]].
在有n个顶点的图中，度值为n-1的顶点叫作主导顶点
在有n个顶点的图中，度值为n-1的顶点叫作'''<font color="#ff8000">主导顶点 Dominating Vertex</font>'''
全局属性
全局属性
*If each vertex of the graph has the same degree ''k'' the graph is called a [[regular graph|''k''-regular graph]] and the graph itself is said to have degree ''k''. Similarly, a [[bipartite graph]] in which every two vertices on the same side of the bipartition as each other have the same degree is called a [[biregular graph]].
*If each vertex of the graph has the same degree ''k'' the graph is called a [[regular graph|''k''-regular graph]] and the graph itself is said to have degree ''k''. Similarly, a [[bipartite graph]] in which every two vertices on the same side of the bipartition as each other have the same degree is called a [[biregular graph]].
如果一个图中的所有顶点的度值都为k，该图被称为'''<font color="#ff8000">''k''-正则图 ''k''-regular graph</font>'''，该图的度值也为k。同样的，同侧每两个顶点都具有相同度值的二分图叫作'''<font color="#ff8000">二分正则图 Biregular Graph</font>'''。
*An undirected, connected graph has an [[Eulerian path]] if and only if it has either 0 or 2 vertices of odd degree. If it has 0 vertices of odd degree, the Eulerian path is an Eulerian circuit.
*An undirected, connected graph has an [[Eulerian path]] if and only if it has either 0 or 2 vertices of odd degree. If it has 0 vertices of odd degree, the Eulerian path is an Eulerian circuit.
当且仅当具有0或2个奇数度的顶点时，无向连通图才具有'''<font color="#ff8000">欧拉路径 Eulerian Path</font>'''。 如果它具有0个奇数度的顶点，则欧拉路径为'''<font color="#ff8000">欧拉回路 Eulerian Circuit</font>'''。
*A directed graph is a [[pseudoforest]] if and only if every vertex has outdegree at most 1. A [[functional graph]] is a special case of a pseudoforest in which every vertex has outdegree exactly 1.
*A directed graph is a [[pseudoforest]] if and only if every vertex has outdegree at most 1. A [[functional graph]] is a special case of a pseudoforest in which every vertex has outdegree exactly 1.
有向图是当且仅当每个顶点的度值最大为1时才是'''<font color="#ff8000">伪森林 Pseudoforest</font>'''。'''<font color="#ff8000">功能图 Functional Graph</font>'''是伪森林的特例，其中每个顶点的度数都恰好为1。
有向图是当且仅当每个顶点的度值最大为1时才是'''<font color="#ff8000">伪森林 Pseudoforest</font>'''。'''<font color="#ff8000">功能图 Functional Graph</font>'''是伪森林的特例，其中每个顶点的度数都恰好为1。