Mathematics Standard • Year 11 • Networks • Lesson 1
Introduction to Networks · Apply
Model a connection system as an undirected graph, then interpret its degree and routes.
Practice
Unless a question says otherwise, treat each network as a simple undirected graph: edges are unordered vertex pairs, with no loops or duplicate edges. Show your reasoning in the answer space; an edge list is enough.
Q1 · Study-group links. Asha (A) worked with Ben (B) and Chen (C); Ben also worked with Dev (D); Chen worked with D. Write V and E, then give each degree. 3 marks
Q2 · Check a route. Using the study-group network, give a two-edge route from A to D. Is A–B–C–D a route? Explain. 2 marks
Q3 · Add a proposed link. A new report lists AC, but AC is already an edge. Should it be added to a simple graph? What if repeated links are allowed? 2 marks
Q1 · Study-group links
V={A,B,C,D}; E={AB,AC,BD,CD}. Each vertex has degree 2; there are 4 links.
Q2 · Check a route
A–B–D uses two edges. A–B–C–D is not a route because BC is not an edge.
Q3 · Add a proposed link
No. A simple graph has at most one edge for each vertex pair. Allowing both would create a multigraph; both edges would count toward the degrees.