A graph is Euler if * (d) It contains an Euler walk. (b) Its disconnected and every vertex has even degree (a) Its connected and every vertex has even degree (c) Its connected and every vertex has odd degree

Q: © Show that it is not possible to create degree 3 and 2 vertices of degree &. graph with 7 verlices…

A: By handshaking lemma, we get that the sum of degrees of all the vertices in a graph is two times the…

Q: 1. Is there a connected graph whose degree are: a. 5, 3, 2, 2, 2, 1, 1

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: I have a graph with 2021 vertices. It is not a tree but there exists some vertex whose removal makes…

A: We know that maximum number of possible edges is 3(n-2)

Q: Graph G has 22 vertices, is simple, connected, and planar, and does not have a circuit of length 4.…

A: Given that,

Q: iph exists. 1. Graph with six vertices of degrees 1,1, 2, 2, 2,3. 2. Graph with four vertices of…

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Q: A trail is a walk that does not repeat an edge. Prove that a trail that repeats a vertex must…

A: Assume that vertex Vk is repeated Let the trail be W: V1V2.....Vk........Vn....Vi.....Vk.......Vj…

Q: 1. Create a connected graph having 8 vertices and 15 edges. 2. Label vertices with A,B,C,D,E, F,G…

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Q: Find one of the graphs with chromatic number 4 that does not have a circuit with length 3

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Q: A tree is a connected graph with no cycle. Use contradiction to prove that every tree with at least…

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Q: 9. Draw two simple connected undirected graphs, each with six nodes, with every node of degree 3,…

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Q: A graph G is Eulerian if and only if All its vertex degrees are even. It is a simple graph that can…

A: Let G be an Eulerian graph.

Q: Prove that a cycle with even number of vertexes is bipartite graph.

A: A bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets U…

Q: A connected multigraph has an euler path if and only if it has Every vertex has even degree Every…

A: Given that  A connected multigraph has an Euler Path if and only if it has.

Q: 4. Prove: "The complement of the graph G is an Eulerian graph whenever G is also an Eulerian graph…

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Q: If an undirected graph has more than two vertices of odd degree, it does not have an Euler path.

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Q: An edge is called a bridge if the removal of the edge increases the number of connected components…

A: We draw a graph without loop, find number of bridges by removing edges.

Q: A cycle that visits every vertex of the graph exactly once is called Euler cycle Hamiltonian cycle…

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Q: Let G be a connected simple graph in which all vertices have degree 4. Prove that it is possible to…

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Q: 1. Prove that a graph is bipartite if and only if it doesn't have any simple circuits of odd order.…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: A connected multigraph has an euler path if and only if it has o Every vertex has odd degree Exactly…

A: Every time a circuit passes through a vertex, it adds twice to its degree. Since it is a circuit, it…

Q: Draw an Eulerian graph which has 5 vertices having one vertex with degree 4 and other vertices with…

A: Given: To draw the Eulerian graph which has 5 vertices having one vertex with a degree 4 and the…

Q: Apply Euler’s Theorems and Fleury’s Algorithm to determine Euler path and Euler circuits in each…

A: (a) Consider the given graph. Specify verticals and their degrees (the degree of a vertex is the…

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: The complete tripartite graph K,, consists of three sets of vertices (of sizes r, s and t), with an…

A: Given that The complete tripartite graph Kr,s,t The graph of K2,2,2 in the following graph Hence,…

Q: A connected multigraph has an euler path if and only if it has Exactly two vertices of odd degree…

A: Every time a circuit passes through a vertex, it adds twice to its degree. Since it is a circuit, it…

Q: Prove the following and make a sketch. a) Prove that every Eulerian graph of odd order has three…

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Q: (7) A connected Eulerian graph has 3 vertices and 7 edges. Show that if one vertex has degree 8,…

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Q: How many Euler paths are there in this graph?

A: The objective is to find the Euler path in the graph

Q: 19 Can a graph with three vertices of degrees 2, 1, 4 exist? Yes No

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Q: An outerplanar graph is a graph that admits a planar embedding with all vertices on the boundary of…

A: Given that an outerplanar graph is a graph that admits a planar embedding with all vertices on the…

Q: #4 with graph

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Q: We say that two graphs are distinct if and only if these two graphs are not isomorphic. How many…

A: Given: Two graphs are distinct if and only if these two graph are not isomorphic. To find: How many…

Q: Consider the graph with 6 vertices of degree 2, 4, 1,1, 6,3, 5. Does the graph exist? Graph does not…

A: NOTE: As given degree of 7 vertices , so we consider number of vertices as 7 ( otherwise question is…

Q: A connected graph has 40 even vertices and no odd vertices. Determine whether the graph has an Euler…

A: A connected graph has 40 even vertices and no odd vertices. according to the Euler theorem of the…

Q: Use Euler's theorem to determine whether the graph has an Euler path (but not an Euler circuit),…

A: Given that, the graph has 102 even vertices and no odd vertices.

Q: 8) A graph has an Euler path and no Euler circuit if A) it is connected and every vertex has even…

A: Given a graph has an Euler path and no Euler circuit.

Q: Either draw a graph with the specified properties or explain why no such graph exists. Graph with…

A: As 3 questions are given , I will solve only the first question, 1.Graph with five vertices of…

Q: True or false: If a connected graph G can be decomposed into exactly k paths then exactly 2k…

A: To Prove: A connected graph can be decomposed into exactly k paths then exactly 2k vertices of G…

Q: Can a simple graph exist with 9 vertices all of degree 5?

A: Handshaking lemma: In any graph, sum of degree of all the vertices is twice the number of edges…

Q: Let G be a connected graph with at least two nodes. Prove that it has a node such that if this node…

A: Consider a connected graph with at least two vertices. choose vertices u,v so that du,v=maximum if…

Q: Which graph is Eulerian? Which graph is not Eulerian but contain ai Eulerian path? Graph - Graph 2…

A: Find your answer below

Q: Prove: “The complement of the graph G is an Eulerian graph whenever G is also  an Eulerian graph of…

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Q: Problem: Let Qn be the hypercube graph on 2" vertices, i.e. the graph whose vertex set is the binary…

A: From the above hypercube, it can be inferred that a vertex is adjacent only to those vertices here…

Q: Which of the following is false? * Hamiltonian cycle can be converted to a Hamiltonian path by…

A: Given that: Hamiltonian cycle and Path.

Q: A graph is called d-regular if every vertex has a degree of d. Let k and n be odd numbers, and prove…

A: Here we have to know the basic concept or the basic theorem before answering the question  THEOREM :…

Q: (g) How many paths of length n exist between vertices 1 and 2 in the graph with adjacency matrix A?

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Q: b) Euler graph of order 5.

A: An Euler graph is a graph if a closed trail is there that passes through every edge of the graph .…

Q: 4. Find the Euler path of the graphs below. Start from one of the vertices that has odd degree.…

A: An Euler path is a trail that starts at any vertex of the graph and traverses each edge of the graph…

Q: 3 with graph

A: The z test are used to measure the mean significance exist between the sample and population. Used…