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→Degree sequence
无向图的度序列是指将其各顶点度值按非递增方式排序，对于上述图是(5,3,3,2,2,1,0)。度序列是'''<font color="#ff8000">图不变量 Graph Invariant</font>'''，因此'''<font color="#ff8000">同构图 Non-isomorphic Graphs</font>'''（两个图中顶点的度值都相同，但形状不同）具有相同的度序列。然而，度序列通常不能唯一地标识一个图，在某些情况下，非同构图具有相同的度序列。
无向图的度序列是指将其各顶点度值按非递增方式排序，对于上述图是(5,3,3,2,2,1,0)。度序列是'''<font color="#ff8000">图不变量 Graph Invariant</font>'''，因此'''<font color="#ff8000">同构图 Non-isomorphic Graphs</font>'''（两个图中顶点的度值都相同，但形状不同）具有相同的度序列。然而，度序列通常不能唯一地标识一个图，在某些情况下，非同构图具有相同的度序列。
--[[用户:CecileLi|CecileLi]]([[用户讨论:CecileLi|讨论]]) 【审校】“无向图的度序列是指将其各顶点度值按非递增方式排序”一句中的“非递增”改为“递减/并不是按递增方式排序的”
The '''degree sequence problem''' is the problem of finding some or all graphs with the degree sequence being a given non-increasing sequence of positive integers. (Trailing zeroes may be ignored since they are trivially realized by adding an appropriate number of isolated vertices to the graph.) A sequence which is the degree sequence of some graph, i.e. for which the degree sequence problem has a solution, is called a '''graphic''' or '''graphical sequence'''. As a consequence of the degree sum formula, any sequence with an odd sum, such as (3, 3, 1), cannot be realized as the degree sequence of a graph. The converse is also true: if a sequence has an even sum, it is the degree sequence of a multigraph. The construction of such a graph is straightforward: connect vertices with odd degrees in pairs by a [[matching (graph theory)|matching]], and fill out the remaining even degree counts by self-loops.
The '''degree sequence problem''' is the problem of finding some or all graphs with the degree sequence being a given non-increasing sequence of positive integers. (Trailing zeroes may be ignored since they are trivially realized by adding an appropriate number of isolated vertices to the graph.) A sequence which is the degree sequence of some graph, i.e. for which the degree sequence problem has a solution, is called a '''graphic''' or '''graphical sequence'''. As a consequence of the degree sum formula, any sequence with an odd sum, such as (3, 3, 1), cannot be realized as the degree sequence of a graph. The converse is also true: if a sequence has an even sum, it is the degree sequence of a multigraph. The construction of such a graph is straightforward: connect vertices with odd degrees in pairs by a [[matching (graph theory)|matching]], and fill out the remaining even degree counts by self-loops.
一般来说，'''<font color="#ff8000">超图 Hypergraph</font>'''的度序列是其顶点度的非递增序列。一个序列是<math>k-graphic</math>，如果它是一些<math>k-uniform</math>超图的度序列。特别是<math>2</math>-graphic序列是图形。决定一个给定的序列是否是<math>k</math>-graphic可以在 <math>k=2</math>的多项式时间内通过Erdős–Gallai定理实现，但是当<math>k\ge 3</math>时该问题可转化为'''<font color="#ff8000">NP完全问题 NP-complete</font>'''(Deza et al. ，2018)。
一般来说，'''<font color="#ff8000">超图 Hypergraph</font>'''的度序列是其顶点度的非递增序列。一个序列是<math>k-graphic</math>，如果它是一些<math>k-uniform</math>超图的度序列。特别是<math>2</math>-graphic序列是图形。决定一个给定的序列是否是<math>k</math>-graphic可以在 <math>k=2</math>的多项式时间内通过Erdős–Gallai定理实现，但是当<math>k\ge 3</math>时该问题可转化为'''<font color="#ff8000">NP完全问题 NP-complete</font>'''(Deza et al. ，2018)。
==Special values==
==Special values==