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Conway's 99-graph problem
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Unsolved problem in mathematics: Does there exist a <a href="/facts/Strongly_regular_graph/0GbdLwSd">strongly regular graph</a> with parameters (99,14,1,2)? <a href="/facts/List_of_unsolved_problems_in_mathematics/RroxGPpP">(more unsolved problems in mathematics)</a> <p>In <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, Conway's 99-graph problem is an unsolved problem asking whether there exists an <a href="/facts/Undirected_graph/kw3eIBUe">undirected graph</a> with 99 <a href="/facts/Vertex_(graph_theory)/WhlWmL3o">vertices</a>, in which each two adjacent vertices have exactly one common neighbor, and in which each two non-adjacent vertices have exactly two common neighbors. Equivalently, every edge should be part of a unique triangle and every non-adjacent pair should be one of the two diagonals of a unique 4-cycle. <a href="/facts/John_Horton_Conway/g3PA1zoK">John Horton Conway</a> offered a $1000 prize for its solution. </p>