Let G be a connected graph which is regular of degreer. Prove that the line graph of G, L(G), is Eulerian.
Let G be a connected graph which is regular of degreer. Prove that the line graph...
A.) Prove that if some graph G is an Eulerian graph, the L(G) {the line graph of G} is also Eulerian. B.) Find a connected non-Eulerian graph for which the line graph is Eulerian.
(a) Let L be a minimum edge-cut in a connected graph G with at least two vertices. Prove that G − L has exactly two components. (b) Let G an eulerian graph. Prove that λ(G) is even.
A connected simple graph G has 16 vertices and 117 edges. Prove G is Hamiltonian and prove G is not Eulerian
Question 13. Prove that if k is odd and G is a k-regular (k - 1)-edge-connected graph, then G has a perfect matching Question 13. Prove that if k is odd and G is a k-regular (k - 1)-edge-connected graph, then G has a perfect matching
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 a connected regular graph with an odd number of vertices is always Eulerian.
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.
2. (a) Let G be a connected non-complete graph with order n 2 3 and diameter d. Prove that the connectivity K(G) of G satisfies d-1 (b) A connected graph is called unicyclic if it contains exactly one cycle. Prove that the edge-connectivity of any unicyclic graph is at most 2. 2. (a) Let G be a connected non-complete graph with order n 2 3 and diameter d. Prove that the connectivity K(G) of G satisfies d-1 (b) A connected...
Let G be a connected non-complete graph with order n 2 3 and diameter d. Prove that the connectivity κ(G) of G satisfies d-1 Let G be a connected non-complete graph with order n 2 3 and diameter d. Prove that the connectivity κ(G) of G satisfies d-1
er (a) Let G be a connected graph and C a non-trivial circuit in G. Prove directly that if an edge ={a, b} is removed from then the subgraph S CG that remains is still connected. Directly' means using only the definitions of the concepts involved, in this case 'connected' and 'circuit'. Hint: If r and y are vertices of G connected by path that includes e, is there an alternative path connecting x to y that avoids e? (b)...