Understand the meaning of graph, vertex (node), edge (arc), loop, degree of a vertex, subgraph, simple graph, complete graph, bipartite graph, directed graph (digraph), weighted graph and network.

A network graph representing five computer servers (labelled \(A\), \(B\), \(C\), \(D\) and \(E\)) and their direct connections is shown in the diagram. (a) State the degree of vertex \(C\). (1 mark) (b) Determine whether the graph is a simple graph. Justify your answer. (1 mark) (c) State whether the subgraph containing only vertices \(A\), \(B\), \(D\) and the edges connecting them forms a complete graph. Justify your answer. (1 mark)

A network represents seven computer terminals, labelled \(A\) through \(G\), connected by data cables in a university computer lab. (a) State the degree of vertex \(D\). (1 mark) (b) Identify whether the network contains any loops. Justify your answer. (1 mark) (c) Determine the total number of edges in the network. (1 mark)

A network graph is shown. Which of the following statements correctly describes this network graph?

A network graph is shown. Which statement correctly describes the graph?

A network diagram represents six computer servers (labelled A, B, C, D, E, F) and the direct cable connections between them. (a) State the degree of vertex C. (1 mark) (b) Calculate the number of edges in a complete graph with 6 vertices, and hence determine how many additional edges would be required to make the given network complete. (2 marks)