In graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.

Related MCQs

• Consider a undirected graph G with vertices { A, B, C, D, E}. In graph G, every edge has distinct weight. Edge CD is edge with minimum weight and edge AB is edge with maximum weight. Then, which of the following is false?
• A complete bipartite graph is a one in which each vertex in set X has an edge with set Y. Let n be the total number of vertices. For maximum number of edges, the total number of vertices hat should be present on set X is?
• A k-regular bipartite graph is the one in which degree of each vertices is k for all the vertices in the graph. Given that the bipartitions of this graph are U and V respectively. What is the relation between them?
• There is no existing relationship between a Hamiltonian path problem and Hamiltonian circuit problem.
• What is the time complexity for finding a Hamiltonian path for a graph having N vertices (using permutation)?
• For a graph of degree three, in what time can a Hamiltonian path be found?
• How many Hamiltonian paths does the following graph have?
• How many Hamiltonian paths does the following graph have?
• A graph has 20 vertices. The maximum number of edges it can have is? (Given it is bipartite)
• Which of the following algorithm can be used to solve the Hamiltonian path problem efficiently?