A Level Further Maths: Decision Maths

If a graph has no loops or multiple edges it is called a _____ graph. - answer-simple What is the minimum number of edges that a connected graph with x vertices can have? - answer-x-1 A complete graph has eight vertices. How many edges does it have? - answer-28 A complete graph has 45 edges. How many vertices does it have? - answer-10 In a particular adjacency matrix, column A is adds up to 7. What is the degree of vertex A in the graph? - answer-7 A network is different to a graph because it has a _____ on each edge. - answer-weight In a particular distance matrix, the sum of all the numbers is 24. Given that the graph is a complete graph, and all sides are 4 units long, state the number of vertices. - answer-3 Any continuous journey around a graph is called a _____. - answer-walk A journey around a graph which never uses an edge more than once is called a _____. If it returns to the starting vertex it is called a closed _____. - answer-trail A trail which does not revisit any vertex is called a _____. - answer-path A closed path (i.e. one that returns to the start) is called a _____. - answer-cycle A connected network has n vertices. How many edges does its spanning tree have? - answer-n-1 Could an edge have a negative weight? - answer-yes 7 towns in a network are connected with 15 straight roads, each road being 5 miles long. What is the maximum possible distance between any two towns? - answer-30 miles