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DominatorVertexList
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DominatorVertexList

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gives the list of dominators of the directed graph g from the root vertex r.

Details

  • DominatorVertexList is also known as immediate dominators.
  • Typically used to analyze and detect dependencies in flow graphs.
  • For a graph g with vertices {u1,u2,…}, DominatorVertexList[g,r] gives a list of vertices {v1,v2,…} where every path from r to ui goes through vi.
  • DominatorVertexList[g,r] returns a list of predecessor vertices vi of vertices ui where vi dominates ui.

Examples

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Basic Examples  (1)Summary of the most common use cases

Give the list of dominators of the directed graph:

In[3]:=3
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https://wolfram.com/xid/0k73oaec6mc92-y8bpmq
Out[3]=3

Scope  (1)Survey of the scope of standard use cases

DominatorVertexList works with directed graphs:

In[1]:=1
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https://wolfram.com/xid/0k73oaec6mc92-5mwujr
Out[1]=1

Properties & Relations  (1)Properties of the function, and connections to other functions

Use DominatorTreeGraph to find the dominator tree of the given graph:

In[6]:=6
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https://wolfram.com/xid/0k73oaec6mc92-2n2wve
In[7]:=7
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https://wolfram.com/xid/0k73oaec6mc92-xk90sh
Out[7]=7
Wolfram Research (2021), DominatorVertexList, Wolfram Language function, https://reference.wolfram.com/language/ref/DominatorVertexList.html.
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Wolfram Research (2021), DominatorVertexList, Wolfram Language function, https://reference.wolfram.com/language/ref/DominatorVertexList.html.

Text

Wolfram Research (2021), DominatorVertexList, Wolfram Language function, https://reference.wolfram.com/language/ref/DominatorVertexList.html.

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Wolfram Research (2021), DominatorVertexList, Wolfram Language function, https://reference.wolfram.com/language/ref/DominatorVertexList.html.

CMS

Wolfram Language. 2021. "DominatorVertexList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DominatorVertexList.html.

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Wolfram Language. 2021. "DominatorVertexList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DominatorVertexList.html.

APA

Wolfram Language. (2021). DominatorVertexList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DominatorVertexList.html

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Wolfram Language. (2021). DominatorVertexList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DominatorVertexList.html

BibTeX

@misc{reference.wolfram_2025_dominatorvertexlist, author="Wolfram Research", title="{DominatorVertexList}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/DominatorVertexList.html}", note=[Accessed: 27-March-2025 ]}

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@misc{reference.wolfram_2025_dominatorvertexlist, author="Wolfram Research", title="{DominatorVertexList}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/DominatorVertexList.html}", note=[Accessed: 27-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_dominatorvertexlist, organization={Wolfram Research}, title={DominatorVertexList}, year={2021}, url={https://reference.wolfram.com/language/ref/DominatorVertexList.html}, note=[Accessed: 27-March-2025 ]}

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@online{reference.wolfram_2025_dominatorvertexlist, organization={Wolfram Research}, title={DominatorVertexList}, year={2021}, url={https://reference.wolfram.com/language/ref/DominatorVertexList.html}, note=[Accessed: 27-March-2025 ]}