Question

The vertex and edge set of a graph is given below. Draw a representation of the graph.

V = {F, G, H, I, J, K, L, M, N, O, P, Q, R}

E = { {F, G}, {F, H}, {F, I}, {F, K}, {G, H}, {H, M}, {H, P}, {I, Q}, {I, R}, {J, R}, {K, M}, {K, O}, {K, R}, {L, Q}, {M, Q} }

Which vertex has the highest degree?

Is this graph connected?

Answer 1

Three vertices have the highest degree: F, H and K.

The graph is not connected.

Explanation:

The degree of a vertex is the number of edges incident on that vertex. In this graph, there are three vertices having the highest degree (4): F, H and K.

The graph is not connected as there aren't any paths joining vertex N with any of the other vertices.