Show that in a simple graph with at least two vertices there must be two vertices that have the same degree.

Q: Graph Algorithm: Prove that if v0 and v1 are distinct vertices of a graph G = (V,E) and a path…

A: Here is Solution for above Problem :: Since given graph G = (V, E) have v0 and v1  are distinct…

Q: Let G be a graph such that every vertex has degree 4 and the number of edges is 12. How many…

A: Actually, graph consisting of edges and nodes.

Q: 1.7 Show that every simple graph has two vertices of the same degree.

A: The answer to the given question is in subsequent steps.

Q: Question 2: Draw a simple undirected graph G that has 11 vertices, 7 edges. Note hand drawing not…

A: INTRODUCTION: The simplest basic data structure is a graph. An undirected graph is made up of nodes…

Q: A graph is connected if O it is not comprised of 2 disjoint pieces O there is a circuit at any…

A: Answer is last option (THERE EXISTS A PATH BETWEEN ANY 2 VERTICES)

Q: A non directed graph G had 8 edges. Find the number of vertices, if the degree of each vertex in G…

A: HI THEREI AM ADDING ANSWER BELOWPLEASE GO THROUGH ITTHANK YOU

Q: either draw a graph with the stated property, or prove that no such graph exists.   A graph on 45…

A: Here in this question we have given a graph with 45 vertices in which 22 vertices have degree 8 and…

Q: Show that every graph with two or more nodes contains two nodes that have equal degree

A: A graph with 2 vertices has either 0 or 1 edges,and in either case, the two nodes have the same…

Q: Let G be a connected planar graph with 32 vertices, 50 edges and degree of each region is k. Find…

A: the value of region as k is calculated in step 2.

Q: 35. Any simple graph with n vertices is connected if it has A. Less than (n)(n-1)/3 edges

A: Given:

Q: 6. Does each of these lists of vertices form a path in the following graph? Which are circuits? What…

A: Step 1: Step 2: Step 3: Step 4:

Q: draw all non isophormic,cycle-free,connected graphs having six vertices

A: Given, draw all non isophormic,cycle-free,connected graphs having six vertices

Q: Draw the following: a. Complete graph with 4 vertices b. Cycle with 3 vertices c. Simple…

A: According to the Bartleby guideline, we are supposed to answer only one question at a time. Kindly…

Q: a d b a) Give the vertex set of the G. b) Give the set of edge of G. c) Find the degree of each of…

A: In this question we have been given with the graph and we have to answer for the graph theory…

Q: For the graph shown below, find articulation vertices and bi-connected components of the graph if we…

A: For the graph shown below,  articulation vertices and bi-connected components of the graph is shown…

Q: True or false: The sum of the degree of the vertices of an undirected graph must be even.

A: An undirected graph consists of vertices (sometimes referred to as nodes) and edges, where the edges…

Q: Let G be a graph with distinct vertices u and v. Assume that u and v have degree three and all other…

A: Let G be a graph with distinct vertices  u and  v such that deg ( u ) = deg ( v ) = 3…

Q: The numbers of edges in these components are 11,5,7,10 and 16. Find the number of vertices and the…

A: 3 edges are removed from a graph G without removing any vertices the resulting graph G0 is a forest…

Q: In an undirected graph, the sum of degrees of all vertices is a. Odd b. Even c. Even and odd both.…

A: Given that In an undirected graph, the sum of degrees of all vertices is a. Odd b. Even c.…

Q: A graph that contains loops and possibly multiple edges is called a Simple graph Multigraph…

A: Question A graph that contains loops and possibly multiple edges is called a 1.Simple graph…

Q: Is it true or false?  If it is true, include a (short, but clear) argument why it is true, and if it…

A: Given four statements and we need to find out if they are true or false.

Q: Draw a simple undirected graph G that has15 vertices, 15 edges.

A: Given:  vertices=15 edges=15

Q: construct a bipartite graph with vertices L,M,N,O,P,Q that is a tree. what is the edge set?…

A: construction of a bipartite graph with vertices L,M,N,O,P,Q that is a tree is given as shown below.…

Q: 5. Vertices: (a, b, c, d, e, f. g} Edges: {{a,b). {a, f). (b, e). (b. g). (c. f). {c. g). (c. d).…

A: vertices {a,b,c,d,e,f,g} edes given draw graph and find adjacent vertices of vertex c find shortest…

Q: Give an example of a graph with an infinite number of vertices and an infinite number of edges that…

A:

Q: Draw an undirected graph with 6 vertices that has an Eulerian Cycle and a Hamiltonian Cycle. The…

A: A Hamiltonian Cycle is a path in a graph that visits every vertex exactly once and ends at the…

Q: Find simple connected graphs with the following vertex degrees if possible. 2 2 2 2 3 3 3 3 4 4 4…

A: Here in this question we have given three graph degree sequence and we have asked to find connected…

Q: Construct a simple graph with vertices A,B,C,D,E,F whose degrees are 3, 1, 1, 2, 3, 2. (For example,…

A: vertices A,B,C,D,E,F whose degrees are 3, 1, 1, 2, 3, 2. 1,2,1 has edge set

Q: 3. Draw a connected graph with 4 vertices, each of degree 3.

A:

Q: V1 V7 V8 V2 e V6 V5 V4 V10 V9 V3

A: Eulerize The process of duplicating existing edges until you arrive at a graph that is connected…

Strongly Connected Components

 A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly connected component (SCC).