Fill in each blank so that the resulting statement is true. A graph that has an edge between each pair of its vertices is called a/an graph. If such a graph has n vertices, the number of Hamilton circuits in the graph is given by the factorial expression !. (Note that there is already factorial expression)

Q: 8. (a) Can you draw a graph with at least two vertices for which all the vertices have different…

A: consider the graph  A has valence 1 Vertex B has valence 2 Vertex C has Valence 3 Vertex D has…

Q: Use graphs to find the set. (-5,0) N[-4,3]

A: Given: The given set is (-5,0)∩[-4,3]

Q: 11. Prove: If G is a simple connected graph where the average degree of the vertices is exactly 2,…

A:

Q: (a) Draw a graph with nodes representing the numbers 1, 2, ⋯ , 10, in which two nodes are connected…

A: Here 10 nodes will be present.

Q: 13. Does the join of two graphs hold commutativity? Illustrate with examples.

A: 13. We need to show whether the join of two garph is commutative or not.  Join of two graphs means…

Q: Show that every graph with n vertices and k edges, n> k has n – k components.

A:

Q: Are these graphs isomorphic? Yes because they have the same number of vertices Yes because they have…

A: Two graphs G1 and G2 are isomorphic if there exists a matching between their vertices so that two…

Q: How many connected components does the following graphs have?

A:

Q: Let A and B each be sets of N labeled as vertices, and consider the bipartite between A and B 1.…

A: Given: A, B be any sets of N labeled vertices in each. Bipartite between the set A and B. To find:…

Q: Suppose G is a simple graph with n > 1 vertices such that every vertex has degree at least (n –…

A: Let G be the simple graph with the vertices n≥1 and every vertex has the degree of at least n-12.…

Q: Suppose that a graph G has n vertices, and all vertices have degree greater than or equal to“,.…

A: Let G be a graph with n vertices. Given that all vertices have degree greater than or equal to n-12.…

Q: 3. In a planar drawing of a graph, each face is bounded by a circuit. Make a planar drawing of a…

A: New graph equivalent to given graph.In which bordered by A-B-C-G-F-Ais in the infinite face.

Q: (a) Draw a graph with nodes representing the numbers 1, 2,..., 10, in which two nodes are connected…

A: To find-  Draw a graph with nodes representing the numbers 1, 2,..., 10, in which two nodes are…

Q: Pick a set of five vertices of H and draw the subgraph induced by that set of vertices H: X10

A:

Q: 9. What is being described by "The smallest set of vertices, A, so that every vertex in the graph is…

A: Solution :-

Q: If a simple graph Gis having 12 vertices and 9 edges then its complement graph G will have O 12…

A:

Q: In each part, either draw a graph with the given specifications or explain why no such graph exists.…

A: The given question has 4 subparts. The solution to the first three questions are given below as it…

Q: A Tree is a disconnected (Not connected) graph without a simple circuit. (Choose correct answer) O…

A: False statement

Q: How many different simple graphs are there om the vertex set [n]?

A:

Q: For which n does the graph Kn contain an Euler circuit? Explain.

A: According to the given information, It is required to find the value of n for which the graph Kn…

Q: oblem 11.69. Prove that in any tournament which does not contain a cycle, some vertex beats every…

A: Let D is a tournament which does not contain cycle. we will use a theorem to prove this  Suppose D…

Q: iii) Show that the sum of the degree of all vertices in a graph is an even integer.

A:

Q: If the given graph is Eulerian, find an Euler circuit in it. If the graph is not Eulerian, first…

A: Euler path and circuit : Euler Path is a path in a graph that visits every edge exactly once. Euler…

Q: Let n be a positive integer. Show that every connected graph on n vertices has at least n – 1 -…

A: This is a problem of Graph Theory.

Q: In the following, shade the por- tion of the Venn diagram that represents the given set:

A: In a Venn diagram, rectangle indicates the universal set. Each circle represents an event. The…

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: Suppose we add two edges in a tree T to form a graph G. How many cycles can be there in G.

A: When 1 edges are added to a tree,  a cycles are created When 2 edges are added to a tree, either 2…

Q: Suppose G is a simple graph with n >1 vertices such that every vertex has degree at least (n – 1)/2.…

A:

Q: A sequence of vertices such that each vertex is adjacent to the next vertex is called a(n) a. length…

A: Given question, A sequence of vertices such that each vertex is adjacent to next vertex is called…

Q: 11. > Prove: If G is a simple connected graph where the average degree of the vertices is exactly 2,…

A:

Q: 62. Each of the accompanying graphs represent the sidewalks to be cleaned in a fancy garden (one…

A: An Euler circuit is a circuit that uses every edge of a graph exactly once. An Euler path starts and…

Q: Does the ff. graph contain a Hamilton circuit? False O True

A:

Q: Fill in each blank so that the resulting statement is true. A graph that is connected and has no…

A: Given statements are filled so that they are made true as shown below.

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: Fill in each blank so that the resulting statement is true. A graph that has an edge between each…

A:

Q: Which of the following CANNOT be an Euler circuit for the graph in #26. BACDAEB EABDCADE ABDEA

A: EB is not an edge  So, BACDAEB is not an Euler circuit. Again the cycle EABDCADE covers all the…

Q: A graph is connected if and only if one vertex is neighbor to all other vertices O True O False

A:

Q: Let Xn be a the number of graphs with vertex set [2n], Every vertex has a degree of 1. What is the…

A: For each Xn, we count graphs that satisfy two conditions: The graph must have a vertex set of 2n…

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: List all circuits that can be drawn from the figure. A circuit must use an edge only once. Start by…

A: The objective is to list all possible circuits starting from length 3 in the figure provided below:

Q: Let {6, 4, 3, 1, 1, 1, 0} be a degree sequence of a simple graph G. How many edges are there in the…

A:

Q: 4. Þescribe each graph below. Explain how many vertices and how many edges it has, and if it is a…

A: Graph theory

Q: Show all possible connected sub graphs of the following graph. How many of them are there refer to…

A: Given: a graph

Q: Use graphs to find the set : [1, 3) ∪ (0, 4)

A:

Q: A graph is defined as a pair (V, E) where V is a finite set of elements called vertices, and E is O…

A: Given that a graph is defined as a pair V,E where V is a finite set of elements called vertices.

Q: Let K, be a graph obtained from K, by deleting one edge. How many subgraphs of K, are isomorphic to…

A:

Q: 1.36. Show that if G is a tree then for any pair of vertices a, b there is exactly one path from a…

A: Given that, G be a tree. As, G be a tree that implies that, G is connected and G has no cycle. Since…

Q: Ali sta naslednja grafa izomorfna? Izberite enega: O Drai ONe dr2i

A: Given: Solution: No, the given graphs are not isomorphic.