Can someone suggest me a good software for drawing graphs? The suggested software should be one which can be used to draw the attached graph (together with mathematical symbols) .
I would also highly recommend Ipe for this purpose. With the caveat being that you have to get creative to insert the curly brackets as shown in your sample image (these can be done with the amsmath package.) I know others also use Tikz/Pgf and like it. I've also previously tried Xy-Pic and pstricks. The advantage of Ipe is that it integrates directly with LaTeX, and let's you design things in a mostly what-you-see-is-what-you-get manner, which can be helpful for more complex images.
One caveat is that Ipe tends to be more difficult to get working in Windows. That may have improved recently, with the availability of high-quality prebuilt binaries.
Thanks everyone for your kind suggestions. I tried most of the suggested softwares and found ipe the best one. Special thanks to Seyyed Aliasghar Hosseini, Imran Khaliq and Darren Strash.