Consider an undirected graph with eight nodes. What is the minimum number of edg
ID: 3757955 • Letter: C
Question
Consider an undirected graph with eight nodes. What is the minimum number of edges that it could have? What is the maximum number of edges that it could have? What is the minimum number of edges required for the graph to be connected? In general, for an undirected graph with n nodes, what is the maximum number of edges that it could have? What is the minimum number of edges required for the graph to be connected? For all parts, do not simply provide answers as a number or expression; you must show the derivation and/or provide an explanation.Explanation / Answer
Let n =8 means n edges in undirected graph.
A. What is the minimum number of edges that it could have?
Let n be number of nodes in an undirected graph, the minimum number of edges that it could have (n-1)(n-2)/2.
Let n=8 be number of nodes in an undirected graph, the minimum number of edges that it could have (8-1)(8-2)/2
= (7 * 6)/2
= 21.
B. What is the maximum number of edges that it could have?
Let n be number of nodes in an undirected graph, the maximum number of edges that it could have (n-1)
Let n=8 be number of nodes in an undirected graph, the maximum number of edges that it could have (8-1)=7.
C. What is the minimum number of edges required for the graph to be connected?
Let n be number of nodes in an undirected graph, the minimum number of edges required for the graph to be connected n(n-1)/2
Let n=8 be number of nodes in an undirected graph, the maximum number of edges that it could have 8*(8-1))/2=28.
D. In general, for an undirected graph with n nodes, what is the maximum number of edges that it could have? What is the minimum number of edges required for the graph to be connected?
Let n be number of nodes in an undirected graph, the maximum number of edges that it could have (n-1)
Let n be number of nodes in an undirected graph, the minimum number of edges required for the graph to be connected n(n-1)/2