(i) If A is connected then B is connected (and vice versa: If B... then A) (ii) If A is simple graph then B is simple graph (and vice versa: If B... then A) (iii) If A contains a cycle then B contains a cycle (and vice versa: If B... then A) (iv) If A is a tree then B is a tree (and vice versa: If B... then A)
The following is a graph theory problem:
Suppose we have a graph A = (X, Y) and a subgraph of A, which is expressed as B = (x, y). x is an element of X and y is an element of Y. A subgraph is plainly described as a graph obtained from A by removing vertices &/or edges. For every following statement determine whether it is true or false. Explain or provide counterexample. Be careful when answering the following questions to leave edges that have their endpoints in B.
(i) If A is connected then B is connected (and vice versa: If B... then A)
(ii) If A is simple graph then B is simple graph (and vice versa: If B... then A)
(iii) If A contains a cycle then B contains a cycle (and vice versa: If B... then A)
(iv) If A is a tree then B is a tree (and vice versa: If B... then A)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
