# Graph Theory

 Network Destinations with their connecting links Euler circuit problems problems questioning routes and backtracking Graph Theory the study of circuit and routing problems graph collection of one or more points(vertices) and the connections between them(edges) Vertices connections on a graph Vertex Connection on a graph {singular} edges connections on a graph eithier straight or curved loop edge that connec ts to itself with only one vertex adjacent vertices two vertices ina graph connected by an edge T/F? A vertex may be adjacent to itself True Degree of a vertex Total number of edges at a vertex How do you find the degree of a vertex? Count the number or segments or arches "coming out" of the vertex path route that passes from one vertex to an adjacent vertex, and each edge connecting an adjacent vertex is used, at most, once Euler path path that uses every edge of a graph exactly once circuit path that ends at the same vertex in which it started Euler circuit circuit that uses every edge of a graph exactly once connected graph in which you can travel from any vertice to any other in the graph disconnected a graph in which is not connected components seperate pieces of a graph that cannot be enlarged while remaining connected bridge edge in a connected graph, in which the removal of would leave behind a graph that is disconnected edge-walker algorithm gives optimal eulerization for a rectangular path If d is the sum of degrees of all vertices and e is the number of edges in a graph, then: (equation) d=2e multigraph more than one edge connecting two vertice Connected graph has a Euler Cycle/Circuit if and only if each of its vertices have an even degree Splicing Is a simple way to make a circuit, rather than using Fleury's Algorithm Authorm1026258 ID34708 Card SetGraph Theory DescriptionGraph theory 6.1 Updated2010-09-15T00:02:05Z Show Answers