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Odd graph
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<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> field of <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, the odd graphs are a family of <a href="/facts/Symmetric_graph/vPVWrnjb">symmetric graphs</a> defined from certain <a href="/facts/Set_system/WbYof7lP">set systems</a>. They include and generalize the <a href="/facts/Petersen_graph/lLRxXpQs">Petersen graph</a>. </p><p>The odd graphs have high <a href="/facts/Odd_girth/rPwRGgxj">odd girth</a>, meaning that they contain long <a href="/facts/Parity_(mathematics)/7zq2UM4V">odd</a>-length <a href="/facts/Cycle_(graph_theory)/Is44edrv">cycles</a> but no short ones. However their name comes not from this property, but from the fact that each <a href="/facts/Edge_(graph_theory)/W0MqKkyE">edge</a> in the graph has an "odd man out", an element that does not participate in the two sets connected by the edge. </p>