Answer to Question #346030 in Discrete Mathematics for M AFAQ

Question

Construct a graph G with 6 vertices {v1, v2, v3, v4, v5, v6} and six edges {e1, e2, e3, e4, e5,

e6} such that

i. e2 is a loop at v2

ii. v2 and v5 are end point of e5

iii. v3 is adjacent to v2

iv. v4 is isolated

v. e3 is parallel to e5

vi. e4 is incident of v1 and v6

Answer 1

i. Loop is an edge that connects a vertex to itself (e₂ connects v₂ and v₂).

ii. v₂ and v₅ are connected by e_2.

iii. There is an edge between v₂ and v₃

iv. v₄ is not an endpoint of any edge (isolated vertex).

v. e₃ and e₅ are incident to the same two vertices v₂ and v₅.

vi. v₁ and v₆ are endpoints of e_4.

We haven't conditions on e₁ and e₆, but one of these edges should connect v₂ and v₃ and noone has v₄ as its endpoint.

So we can construct the next graph G: