Show that a connected regular graph with an odd number of vertices is always Eulerian.
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.
A connected simple graph G has 16 vertices and 117 edges. Prove G is Hamiltonian and prove G is not Eulerian
Let G be a connected graph with m 2 vertices of odd degree. Prove that once is m/2. Let G be a connected graph with m 2 vertices of odd degree. Prove that once is m/2.
Show that in any graph it is not possible for there to be an odd number of odd degree vertices.
7.5 (i) Prove that, if G is a bipartite graph with an odd number of vertices, then G is non-Hamiltonian. (ii) Deduce that the graph in Fig. 7.7 is non-Hamiltonian. Fig. 7.7 (iii) Show that, if n is odd, it is not possible for a knight to visit all the squares of an n chessboard exactly once by knight's moves and return to its starting point.
Let G be a connected graph which is regular of degreer. Prove that the line graph of G, L(G), is Eulerian.
need help with a and b in this graph theory question Let n >k> 1 with n even and k odd. Make a k-regular graph G by putting n vertices in a circle and connecting each vertex to the exact a) Show that for all u,v there are k internally disjoint u, v-paths (you (b) Use the previous part, even if you did not prove it, to show that the e vertex and the k 1 closest vertices on either...
Choose the true statement. If a graph G admits an Eulerian path, then G is connected. If a graph G admits an Eulerian path, then G admits a Hamiltonian path. If a graph G admits a Hamiltonian path, then G admits an Eulerian path. the four other possible answers are false If a graph G is connected, then G admits an Eulerian path.
true or false Can a simple connected graph of n vertices and n-1 edges admit a chain or an Eulerian turn.
Give a short proof for why every graph has an even number of vertices of odd degree.