3 votes 3 votes Let G(V,E) be a simple graph. Let G’(V,E’) be a graph obtained from G such that (u,v) is an edge in G’ if (u,v) is not an edge in G. Which of the following is true? At least one of G or G’ are connected. G is necessarily disconnected. Both G and G’ are disconnected. None of the above. vivek_mishra asked Feb 15, 2021 vivek_mishra 556 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes I think the Answer is (A). I tried to draw few example graph and checked it out. But open to suggentions and corrections Agrek11 answered Feb 16, 2021 Agrek11 comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Since (u,v) is an edge in G’ and (u,v) is not an edge in G it is possible that the G’ be the complement of the G then according the property a connected graph complement can be connected or disconnected so I think it is (A) shefaliPr answered Mar 19, 2021 shefaliPr comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Option A will be true and necessarily true always. Here graph G’ is complement of graph G. So even if G is completeyly disconnected, G’ has to be connected of vice versa. rish1602 answered Jul 2, 2021 rish1602 comment Share Follow See all 0 reply Please log in or register to add a comment.