# Math Help - Graph Theory: A has 15 edges, Ā has 13 edges, how many vertices does A have?

1. ## Graph Theory: A has 15 edges, Ā has 13 edges, how many vertices does A have?

Discrete Math: Graph Theory #54.
If A is a simple graph with 15 edges, and Ā has 13 edges, how many vertices does A have?

Can anyone give me the answer and how to arrive at it?

Thanks a bunch,
Yvonne

2. Originally Posted by yvonnehr
Discrete Math: Graph Theory #54.
If A is a simple graph with 15 edges, and Ā has 13 edges, how many vertices does A have?

Can anyone give me the answer and how to arrive at it?

Thanks a bunch,
Yvonne
do you know this statement?

Let $\overline{G}$ be the complementary graph of $G$. Then
$|E(\overline{G})| + |E(G)| = \left({\begin{array}{c} |V(G)| \\ 2 \end{array}}\right)$

3. ## Equation -> Handshaking Theorem?

Originally Posted by kalagota
do you know this statement?

Let $\overline{G}$ be the complementary graph of $G$. Then
$|E(\overline{G})| + |E(G)| = \left({\begin{array}{c} |V(G)| \\ 2 \end{array}}\right)$
I don't believe I have seen this. Is this related or some rendition of the Handshaking Theorem?
-Ivy

4. i dont think so.. we discussed this as a remark in graph operations..

Originally Posted by kalagota
do you know this statement?

Let $\overline{G}$ be the complementary graph of $G$. Then
$|E(\overline{G})| + |E(G)| = \left({\begin{array}{c} |V(G)| \\ 2 \end{array}}\right)$
Tell me I am reading this right.

The sum of the cardinality of (edges) G and G-compliment equals to the cardinality of (vertices) G.

Sorry if I am not getting this correctly. It is very late for me. :-) You know how it goes.

6. Originally Posted by yvonnehr
Tell me I am reading this right.

The sum of the cardinality of (edges) G and G-compliment equals to the cardinality of (vertices) G.

Sorry if I am not getting this correctly. It is very late for me. :-) You know how it goes.
... cardinality of (vertices) G taken 2..

EDIT: that is the usual combination formula..