A graph G is called self complementary iff G is isomorphic to its complement. Let X be a self complementary graph. Which of the following is a viable possibility with regards to the connectivity of X and X', where X' denotes the complement of X,
Option a) Both must be disconnected
b) X is connected X’ disconnected
c)X is disconnected and X’ connected
d)both are connected
answer d
I just want to verify this explanation before assuming that it is correct.
solution given by them
Firstly we know that if two graphs Gi and G, are isomorphic, then either both of them will be connec.d, or both will be disconnected, and it's easy t gue that a situation like option (b) and (c) can never happen as they are isomorphic. Now the option (a) violates the theorem "at least one of G and G' must be connected" so (a) is also ruled out. So the only viable possibility is option (d). Note that a question based on this concept can probably come M GATE, and they can frame it as "Every self complementary graph is corunected" or "Some self complementary graphs are discormected". So be prepared to answer such questions. So the conclusion is "Every sell complementary graph is cormected". So option (d) is the correct answer.
