DM.2† If is a connected graph and all its valences are even, then has an The student will use problem solving, mathematical communication, G G Euler circuit. mathematical reasoning, connections, and representations to Pairs of routes (circuits) correspond to the same Hamilton circuit Determine whether a has an Euler circuit or path, and because one route can be obtained from the other by traversing the determine it, if it exists. vertices in reverse order. Determine whether a has a Hamilton circuit or path, and There are Hamilton circuits. determine it, if it exists. A multigraph is connected if is a path between every pair of Count the number of Hamilton circuits for a complete graph with n vertices. vertices. Use an Euler circuit algorithm to solve optimization problems. Standard should be included in a one-semester course in Discrete Mathematics. †
DM.2† If G is a connected graph and all its valences are even, then G has an Euler circuit. Pairs of routes (circuits) correspond to the same Hamilton circuit because one route can be obtained from the other by traversing the vertices in reverse order. There are Hamilton circuits. A multigraph is connected if is a path between every pair of vertices. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Determine whether a has an Euler circuit or path, and determine it, if it exists. Determine whether a has a Hamilton circuit or path, and determine it, if it exists. Count the number of Hamilton circuits for a complete graph with n vertices. Use an Euler circuit algorithm to solve optimization problems. † Standard should be included in a one-semester course in Discrete Mathematics.