Give a condition that is sufficient but not necessary for an undirected graph not to have an Eulerian Cycle. Justify your answer.
Give a condition that is sufficient but not necessary for an undirected graph not to have an Eulerian Cycle. Justify you...
1. Give a condition that is necessary but not sufficient for an undirected graph to have an Eulerian Path. Justify your answer. 2. Give a condition that is sufficient but not necessary for an undirected graph not to have an Eulerian Cycle. Justify your answer.
1- Give an example (by drawing or by describing) of the following undirected graphs (a) A graph where the degree in each vertex is even and the total number of edges is odd (b) A graph that does not have an eulerian cycle. An eulerian cycle is a cycle where every edge of the graph is visited exactly once. (c) A graph that does not have any cycles and the maximum degree of a node is 2 (minimum degree can...
6.Given a graph G: 2 5 _ 10_ Eulerian cycle is
Given an undirected connected graph so that every edge belongs to at least one simple cycle (a cycle is simple if be vertex appears more than once). Show that we can give a direction to every edge so that the graph will be strongly connected. Please write time complexity.
3. A Unicvcle Problem Prove that a cycle exists in an undirected graph if and only if a BFS of that graph has a cross-edge. (**) Your proof may use the following facts from graph theory . There exists a unique path between any two vertices of a tree. . Adding any edge to a tree creates a unique cycle.
04. Convert the following instance of Hamiltonian cycle problem in a directed graph to an instance of Hamiltonian cycle problem in undirected graph h) 04. Convert the following instance of Hamiltonian cycle problem in a directed graph to an instance of Hamiltonian cycle problem in undirected graph h)
Look up the definition of a biconnected undirected graph on Wikipedia. Give a one sentence definition based on induced sub-graphs. Start your definition with “An undirected graph G = (V, E) is biconnected, if . . . ” (b) For a directed graph G = (V, E), its underlying undirected graph is obtained by replacing every directed edge (u, v) with an undirected one {u, v}. (If (u, v) and (v, u) are both in E, then the underlying undirected...
Give an example or explain why no such example exists: A regular eulerian graph with an even number of vertices and an odd number of edges.
Prove that an undirected graph is bipartite iff it contains no cycle whose length is odd (called simply an "odd cycle"). An undirected graph G = (V,E) is called "bipartite" when the vertices can be partitioned into two subsets V = V_1 u V_2 (with V_1 n V_2 = {}) such that every edge of G has one endpoint in V_1 and the other in V_2 (equivalently, no edge of G has both endpoints in V_1 or both endpoints in...
6 necessary and sufficient condition for person centered change