Let vertex sets V1 and V2 be defined by V1 1 2 3 and V2 a b

Let vertex sets V1 and V2 be defined by V1= {1, 2, 3} and V2 = {a, b, c}. Let E1 = { { 1, 2}, {2, 3} }, and let E2 = { {a, b}, {b, c} } be the edge sets corresponding to the vertex sets V1 and V2, respectively. Write a function f that is a bijection from V1 to V2.

Solution

The function is said to be bijection, if the function from V1->V2 is both one-to-one and onto i.e. the function will have exactly one value corresponding to the other side value

F = { {1,a}, {2,b} , {3,c} }

The function is one-one mapping since 1,2 and 3 all are mapped to only one element and the complete set V2 is covered in the function, hence the above function satisfy the property of the bijection function