Pick a set of five vertices of G and draw the subgraph induced by that set of vertices G:

Q: Prove that if G is a graph with spanning tree T and e is an edge of G that is not in T, then the…

A: Given that G is the graph with spanning tree T and e is an edge of G that is not in T Let x and y be…

Q: 3. Find the tree and tree cover of Petersen graph. ***** *****

A: The Petersen Graph

Q: In graphing, prove that at least one of G and it's complement, G', is connected.

A:

Q: Prove that every maximal matching in a graph G has at least a'(G)/2 edges.

A:

Q: Give an example to show that if P is a (u, v)-path in a 2-connected graph G, then G does  not…

A: To show that if P is a u,v-path in a 2-connected graph G, then G does not necessarily contain a…

Q: Let G = (V, E) be a connected graph. Use induction to show that if G contains exactly |G| = |V|.…

A: Suppose G=(V,E) be a connected graph, also let that G contains one cycle. Then we show that G=V

Q: (a) If T is a tree with at least 2 vertices, show that x(T) = 2.

A: The given solution is only for part (a) of the question, please resubmit rest of the parts as…

Q: Euler cycle.

A: AnswerSuppose we have some simple graph G, with odd n>, 1 nodes, and that this graphhas an Euler…

Q: Let G be a connected graph with n(G) ≥ 2. Show that G at least 2 vertices which are not cut-vertices…

A:

Q: complement

A:

Q: Let G = (V, E) be a graph (no loops, no multi-edges, undirected, as always. Let d be the smallest…

A: ANSWER:

Q: Let G be a planar graph in which every face is either a triangle or a pentagon. If G has 12…

A: It is given that Let G be a planar graph in which every face is either a triangle or a pentagon. If…

Q: simple path in G from v0 to v1

A:

Q: G is a graph on n 21 vertices such that both G and its complement have an Euler trail. (Recall that…

A: To do: Draw a simple graph G such that "G is a graph with n≥1 vertices such that both G and its…

Q: Give an example to show that if P is a (u, v)-path in a 2-connected graph G, then G does not…

A:

Q: Show that if a simple graph G ha

A: To prove that if a simple graph G has n vertices and at least n edges, then G must contain a cycle.

Q: Pick a set of five vertices of J and draw the subgraph induced by that set of vertices d J:

A:

Q: Determine whether G and H are isomorphic? Also find Euler circuit, Euler trail and Hamiltonian…

A: The isomorphism of graph is given below. To show graph contains  Euler circuit and path we use…

Q: Let L be the set of undirected graphs. Prove that L is in NL.

A: Let L be the set of undirected graphs. A undirected graph is bipartite if its nodes can be divided…

Q: The graph of g con

A: Consider the graph below

Q: Let G be a graph with n vertices. Prove that if G is connected and has n 1 edges, then G is a tree.…

A:

Q: The set of all finite connected simple graphs is countable. O true O false

A: Here the given statement is 'the set of all finite connected simple ghaph is countable'

Q: Let G be a connected graph and e and edge of G. Prove that k(G) = k(G - e) + k(G/e). Here k(G)…

A: Given  G be a connected graph and e an edge of G  we have to prove that kG=kG-e+kG/e here k(G)…

Q: . Find a spanning tree for each g a h b d a)

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Prove the following theorem: If the graph G is a tree then there is a unique path connecting any two…

A:

Q: Let G be a pseudograph with 6 vertices. If G is having 3 loops and no parallel or multiple edges,…

A: For the given statement

Q: 2. Prove that the size of every k-chromatic graph is at least (

A: Consider the provided question, According to you we need to solve only (2). (2) We need to prove…

Q: Let's consider an undirected graph G = that for any vertices, i, j E I and there is no edge between…

A: Given: G = V , E is an undirected graph. An independent subset is a subset I ⊂ V such that for any…

Q: graphing, prove that at least one of G and it's complement, G', is connected.  Draw G and its…

A: If G is connected then nothing have to prove.

Q: 5. For any graph G with six vertices, then G or its complement Ġ contains a triangle.

A: The solution for the above question is as shown below.

Q: Let G be a connected, undirected graph, and let V be the set of all vertices in G. Define a relation…

A:

Q: prove If G is a plane graph with n vertices, m edges and r regions, then n - m + r = 1 + k(G).

A:

Q: Show that every simple graph on n vertices is isomorphic to a subgraph of Kn.

A: We need to prove that every simple graph on n vertices is isomorphic to a subgraph of Kn (complete…

Q: Prove that if G = (V, E) is a connected graph such that |E |V| – 1, then G is a tree. %3D

A:

Q: A. If a simple graph G on 30 vertices has at least 301 edges, then its chromatic number is at least…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 2. Construct a multigraph of order 6 and size 7 in which every vertex is odd.

A:

Q: 5. Are the following directed graphs isomorphic? Provide an isomorphism if they are or an argument…

A: To find an directed isomorphic we should first check if the given graphs are isomorphic or not, if…

Q: Let G be a pseudograph with 6 vertices. If G is having 3 loops and no parallel or multiple edges,…

A: 18 Option (a) is correct.

Q: Draw graph G and its complement, showing that at least one of G and it's complement, G', is…

A: Suppose G is disconnected. We want to show that G¯ is connected. So suppose v and w are vertices. If…

Q: Show that if an edge e is in a closed, trail of G, then e is in a cycle of G

A: Use the following definitions, to obtain the solution. A trail is a sequence of vertices and edges…

Q: d) Draw the subgraph G – E([{a, b, c, x}]) of G. e) Draw a spanning subgraph of G that is connected…

A: Please find the full answer in nextStep

Q: Let G be a graph with v vertices and e edges. Let M be the maximum degree of the vertices of G, and…

A: We are given a G graph G with v number of vertices and e number of edges in the graph. we are also…

Q: Prove that if G is a graph of order p and has size greater than ¹) then G is connected. 2

A:

Q: 1. Let C(G,k) denote the decision problem of whether the undirected graph G = subset of vertices V'…

A: Let C(G,k) denotes the decision problem, Let G is the given graph and k be the subset of the graph…

Q: Let G be a graph and let v and w be vertices in G. (a) A walk from v to w is _____. (b) A trail from…

A: We need to define (i) walk (ii)trail (iii) path (iv) closed walk (v) circuit (vi) simple circuit…