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"in a connected graph" vs "on a connected graph"

Both 'in a connected graph' and 'on a connected graph' are commonly used in English, but they are used in slightly different contexts. 'In a connected graph' is used when referring to properties or elements that exist within the graph itself, while 'on a connected graph' is used when discussing actions or operations that are performed on the graph.

Last Updated: April 01, 2024

in a connected graph

This phrase is correct and commonly used in English when referring to properties or elements that exist within the graph itself.

Use 'in a connected graph' when discussing properties, elements, or characteristics that are part of the graph structure itself.

Examples:

  • In a connected graph, every pair of vertices is connected by a path.
  • The concept of connectivity is important in a connected graph.

Alternatives:

  • within a connected graph
  • inside a connected graph
  • among the vertices of a connected graph
  • amidst a connected graph
  • amid a connected graph

on a connected graph

This phrase is correct and commonly used in English when discussing actions or operations that are performed on the graph.

Use 'on a connected graph' when describing actions, operations, or analyses that are carried out with respect to the graph.

Examples:

  • We can perform various algorithms on a connected graph.
  • The shortest path algorithm works well on a connected graph.

Alternatives:

  • with a connected graph
  • using a connected graph
  • for a connected graph
  • regarding a connected graph
  • in relation to a connected graph

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