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For a graphG, the switched graphS
v
(G) ofG at a vertexv is the graph obtained fromG by deleting the edges ofG incident withv and adding the edges of
incident withv. Properties of graphs whereS
v
(G) ≅G or
are studied. This concept is extended to the partial complementS
H
(G) where H
. The investigation here centers around the existence of setsH for whichS
H
(G) ≅ G. A parameter is introduced which measures how near a graph is to being self-complementary.
