The definition itself says **Simple graph** it can't have self loops

**Simple graph**: No self loop & No Multiedges between 2 vertices

**Multi graph**: Can have multieedges between 2 vertices but no self loop

**General graph or Pseudograph**: Can have both

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The complementary graph G' of a simple graph G has the same vertices as G. Two vertices are adjacent in G' if and only if they are not adjacent in G. Define Qn' (Hypercube complement).

Answer given :-The graph whose vertices are bit strings of length n and two vertices are adjacent if the bit string represented by them differe by more than one bit.

I want to understand that whether the complement graph will have self loops?Because the answer given doesn't consider self loops.I mean why are we not considering the bit strings that are differing by 0 bit,as these are also not there in original graph ,so it must be in complementary graph?

Answer given :-The graph whose vertices are bit strings of length n and two vertices are adjacent if the bit string represented by them differe by more than one bit.

I want to understand that whether the complement graph will have self loops?Because the answer given doesn't consider self loops.I mean why are we not considering the bit strings that are differing by 0 bit,as these are also not there in original graph ,so it must be in complementary graph?

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They are talking about 2 adjacent vertices,if there was and edge in G then it can't be there in G' .So if we take 2 vertices v1 and v2 ,if there were an edge between them in G it shouldn't be there in G'

Moreover when you do G U G' you should get complete graph. Even complete graph can't have self loop

Moreover when you do G U G' you should get complete graph. Even complete graph can't have self loop

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