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I was reading a topic on wikipedia. There a product "corona product" was defined as :

Corona product of graphs $G_1$ and $G_2$, is the graph which is the disjoint union of one copy of $G_1$ and $|V_1|$ copies of $G_2$ ($|V_1|$ is the number of vertices of $G_1$) in which each vertex of the copy of $G_1$ is connected to all vertices of a separate copy of $G_2$.

What I am trying is... Suppose I take graph $G_1$ on 4 vertices. So, according to definition, I have to take 4 copies Of graph $G_2$, say $H_1,H_2,H_3, H_4$ and vertices of $G_1$ as $v_1,v_2,v_3,v_4$. What I understood about the product is that I will join $v_1$ with every copy of $H_1$ only, $v_2$ with every copy of $H_2$ only and so on..

Am I right in performing the product? If not, then please rectify me. Thanks a lot.

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Yes. I was unable to find the original paper, but all other articles do what you describe. Please note, that there is also a different version, the edge corona product (where you add $|E_1|$ copies of $G_2$). $G_1$ is usually called the center graph, while $G_2$ is named outer graph. In the following picture $G_1$ is yellow and $G_2$ is red.

$\hspace{70pt}$enter image description here

I hope this helps $\ddot\smile$

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  • $\begingroup$ @dtdarek ... So your figure is based when we take |V(G1)| copies of graph $G_2$. Am I right Sir? Thanks a lot for ur response sir $\endgroup$
    – monalisa
    Jul 29, 2013 at 5:49
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    $\begingroup$ @monalisa We have $1$ copy of $G_1$ (yellow) and we have $|V(G_1)|$ copies of $G_2$ (red). Does this answer your question? $\endgroup$
    – dtldarek
    Jul 29, 2013 at 5:54
  • $\begingroup$ yeah sir... i understood earlier too :) wanted to make it sure... thanks ... $\endgroup$
    – monalisa
    Jul 29, 2013 at 5:56
  • $\begingroup$ @dtldarek May I ask one thing? How you managed to draw such a beautiful graph? MS Word or something else? $\endgroup$
    – monalisa
    Aug 5, 2013 at 12:18
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    $\begingroup$ @monalisa Thank you for the compliment, mostly I use Inkscape, very convenient tool. Sometimes (like here) I also use a text editor and some scripting (svg, the Inkscape's base format, is xml-based and as such very easy to manipulate). $\endgroup$
    – dtldarek
    Aug 5, 2013 at 15:11

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