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this theorem of eigenvalue of bipartite graph the fist direction is proof but i need the second one as picture
( graph G with at least one edge is bipartite if and only if it’s spectrum is symmetrical with respect to zero) First one direction of this theorem is proved in picture, my question the the second direction of theorem (if G has spectrum is symmetrical with respect 0 then G is bipartite graph)

enter image description here

Second one: the opposite direction, i don't know how i start

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  • $\begingroup$ The two pictures that you've uploaded are the same $\endgroup$ – Omnomnomnom Sep 16 '17 at 3:17
  • $\begingroup$ It's not clear what "i need the second one as picture" is supposed to mean $\endgroup$ – Omnomnomnom Sep 16 '17 at 3:19
  • $\begingroup$ I edit the question, i expected it clear now $\endgroup$ – Maryam Fasfous Sep 16 '17 at 3:22
  • $\begingroup$ Now it's at least clear what you're asking. However, you should still provide some context to your question (otherwise, it is likely that your question will be closed). What are your thoughts on the problem? What have you tried? $\endgroup$ – Omnomnomnom Sep 16 '17 at 3:27
  • $\begingroup$ Again i edit the question, i hope it's clear $\endgroup$ – Maryam Fasfous Sep 16 '17 at 3:42

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