Answer to Question #346030 in Discrete Mathematics for M AFAQ

Question #346030

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

Expert's answer

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

ii. v2 and v5 are connected by e2.

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 e4.

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:

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