If I have graph $G=(V,E)\\$

What is the meaning of $|G|$? (The cardinality of G).

I'd like to know few words about it.

Thank you!

  • 4
    $\begingroup$ $|V|{}{}{}{}{}$. $\endgroup$ – Andrés E. Caicedo Jul 13 '13 at 16:54
  • $\begingroup$ So, it's just the amount of the vertices? $\endgroup$ – CS1 Jul 13 '13 at 16:55
  • $\begingroup$ That is the standard use. $\endgroup$ – Andrés E. Caicedo Jul 13 '13 at 16:55
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    $\begingroup$ Thank you so much! you helped me a lot. $\endgroup$ – CS1 Jul 13 '13 at 17:07

Generally, for a given graph $\,G=(V,E),\;$ the standard meaning of $|G|$ is simply $$|G| = |V|$$

  • 2
    $\begingroup$ While we're on the subject, a few authors write $\|G\|$ to denote the number of edges. $\endgroup$ – Austin Mohr Jul 13 '13 at 16:59


|V| = number of vertices or graph order.

|E| = number of edges or graph size.

Some like to use |G| to mean the graph order though.


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