Is this statement about the chromatic number true? Please give some prove and brief explaination: If A and B are graphs on the same vertex-set, then χ(A ∪ B) ⩽ χ(A) + χ(B).

Q: ery set of vertices in a graph is biconnected if they are connected by two disjoint paths. In a…

A: To show that a graph lacking articulation points is biconnected, we need to prove that any set of…

Q: 2.)Is K6 planar? Explain

A:

Q: 1. Let G be a tree and let L be the set of leaves in G (the vertices of degree 1). (a) If G contains…

A: Spanning Tree A spanning tree is a sub-graph of an unguided connected graph that has all of the…

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: you think finding the "longest path" from p to q can be solved in polynomial time? Given

A: You can solve this using  DFS or applying BFS twice

Q: (a) Recall that the path graph on n vertices has vertex set V = {1,.., n} and edge set E = {{i,i+1}…

A: According to the information given:- We have to recall that path graph on n vertices has vertex set…

Q: say a R-colorin assign colors to vertices of G such that for every edge (v, w) E E, the color of v…

A: It is defined as a common data structure that consists of a finite set of nodes (or vertices) and a…

Q: Compute the vertex set V and edge set E of the graph G=(V,E) whose Prufer Code is (1,2,3,4,5,5)…

A: Vertices in the graph would be equal to the number of terms in prufer code +2.

Q: Every strongly connected graph is Eulerian. There is a series of lowercase letters (a-z) that…

A: A directed graph is graph, a set of objects that are connected together.

Q: path between any two vertices. v) If G is connected, then G is a tree if and only if G contains at…

A: A graph which has only one vertices between all nodes of a graph is called as tree. A tree can be…

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: can stroll to any vertex associated by an edge with your present vertex. On each edge, there are…

A: Here have to determine about number of shows problem statement.

Q: Which values of |V| does a complete graph on |V| vertices have an Euler Tour   What is ϕ (18)?…

A: We need to answer: Which values of |V| does a complete graph on |V| vertices have an Euler Tour What…

Q: How do I do this?  We say a graph G = (V, E) has a k-coloring for some positive integer k if we can…

A: Given: How do I do this?  We say a graph G = (V, E) has a k-coloring for some positive integer k if…

Q: Give a pair of non-isomorphic undirected graphs each with six vertices where every vertex has…

A: Introduction: Edges in undirected graphs are those without a direction. Each edge can be crossed in…

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: A graph is biconnected if every pair of vertices is connected by two disjoint paths. An articulation…

A: Introduction Biconnected: An interconnected graph is considered biconnected in graph theory if…

Q: Determine whether the following assertion is true or false; if it is true then prove it, and if it…

A: We are given an assertion on Euler cycle, we will see if the assertion is true or false. Please…

Q: Give a definition of Graph Embedding, Planar Embedding. Is the following graph a planar graph?…

A:

Q: 4. Run the Bellman-Ford algorithm on the directed graph given blow, using vertex z as the source. In…

A: please see the next steps for solutions.

Q: 4. Let G=(V, E) be the following undirected graph: V = {1, 2, 3, 4, 5, 6, 7, 8} E = {(1, 7) (1, 4),…

A: An undirected graph is a graph, i.e., a set of objects (called vertices or nodes) that are connected…

Q: Suppose that G is an unconnected graph that consists of 4 connected components. The first component…

A: Euler Graph: A linked graph created by Euler. If there is a closed trail that contains every edge of…

Q: 3. For the graph G= (V, E), find V, Ene all parallel edges, all loops and all isolated verfices and…

A: Solution 1: no given any self loop.

Q: Consider the following figure and explain the answer to the ollowing questions. Consider the…

A: We could see in the matrix representation from a to b as 0 whereas we can see b to a as 1  If this…

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: What is the minimum number of edges on a strongly connected diagraph with n vertices?

A: For an adjacency matrix, where the  elements are either 1 (to indicate the presence of an edge) or 0…

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: A graph is biconnected if every pair of vertices is connected by two disjoint paths. An articulation…

A: Biconnected: In graph theory, a connected graph is said to be biconnected if removing any one…

Q: nodes “V" is a vertex cover. The removal of V from the graph destroys every edge. This is the…

A: Here explain about vertex cover…

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: Biconnected refers to any pair of vertices in a graph that are connected by two distinct pathways. A…

A: Biconnected: In graph theory, a connected graph is said to be biconnected if removing any one vertex…

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…

Q: To determine If a graph contains a circuit that starts and ends at a vertex v, does the graph…

A: Simple Circuit: A circuit with no repeated vertices except the first and the last vertex. Consider a…

Q: 2 An article from the fifties describes two problems with corresponding algo- rithms: to connect all…

A: First problem will be solved using Floyd warshall. It is used to find shortest part or minimum total…

Q: Shown below is a properly colored graph, with vertex set [6], that has all the odd numbers orange…

A: Lets see the solution.

Q: Given two vertices s and t and a path connecting them, use the knowledge that none of the vertices…

A: Let's assume that we have a graph G that doesn't contain any articulation points. We will prove that…

Q: Write a topological order of vertices of above graph and illustrate your method.

A: Answer: We need to write the what are the topological order for the given graph. so we will see in…

Q: [1] X(G) for each of the following graphs G: (i) K6; (ii) C5; (ii) Pô; (iv) K2,3; (v) K2 +(2K3).…

A: According to the information given:- We have to write down the edge and vertex connectivity of given…