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4. Prove that a complete graph with nvertices contains n(n 1)=2 edges. 5. Prove that a nite graph is bipartite if and only if it contains no cycles of odd length. 6. Show that if every component of a graph is bipartite, then the graph is bipartite. 7. Prove that if uis a vertex of odd degree in a graph, then there exists a path from uto another

6 P11. Run Prim's algorithm on this graph, to produce the minimum spanning tree (MST) starting from vertex 5. Fill out the table below with edges in the order in which they are selected by the algorithm and added to the MST. For each edge list the vertices and its weight, e.g. (2,5,14) Fill in the dist/parent table as in class.

Do not forget to justify your answers in terms which could be understood by people who know the background theory but are unable to do the questions themselves. All graphs, in the questions below, are understood to be nite ordinary graphs. Note to MATH 123 Fall 2017 students: Questions 11 and 14 involve the notion of graph isomorphism.

Write down the co-ordinates of the other point on the graph of y (i) (iii) The equation f(x) x2 can be written as Show that p —1 and q — On the grid opposite, draw the graph of y x2 for Using your graphs, solve the equation x3 —x -20= The diagram shows a sketch of the graph of y P is the point (n, 0). Write down the value of n. 0. NOT TO -20.

Graph Theory MCQ Questions and Answers Pdf 1. In which tree, for every node the height of its left sub tree and right sub tree differ at least by one? a. AVL tree b. Binary search tree c. Complete tree d. Threaded binary tree Ans: A 2. A graph in which all nodes are of equal degree is called a. Multigraph b. Non regular graph c. Regular graph d.

Quadratic Graphs Name: _____ Instructions • Use black ink or ball-point pen. • Answer all questions. • Answer the questions in the spaces provided – there may be more space than you need. • Diagrams are NOT accurately drawn, unless otherwise indicated. • You must show all your working out. Information

2 MAS 341: GRAPH THEORY 2016 EXAM SOLUTIONS 6 Marks, 2 for each part, 1 for right answer but incomplete justi cation. Proof. Gis not Eulerian, as it has 4 vertices with odd degree (namely 3). Gis not Hamiltonian { locally near each of the vertices of degree 2, a Hamiltonian path would have to just be forced to be straight through. Together ...

Graph Theory Questions - Free download as PDF File (.pdf), Text File (.txt) or read online for free. This document contains 28 multiple choice questions about graph theory concepts such as planar graphs, non-planar graphs, minimum spanning trees, chromatic numbers, and properties of trees and cycles. It also includes diagrams of sample graphs to aid in visualizing the concepts being tested.

For each of the following degree sequences, prove that a simple graph with 7 vertices exists or does not exist by either drawing such a graph or showing mathematically that such a graph is impossible. 1.1,1,2,3,4,5,6. 2.3,3,3,3,3,3,6. 3.2,3,4,4,4,4,5. We are told the graphs must be simple graphs, so there are no loops or repeated edges.

(b) Suppose G is a connected graph which contains no cycles of odd length. Choose v0 2 V(G) and let T be a spanning tree of G rooted at v0. Let X = fv 2 V(G) : distT(v0;v) is eveng and Y = fv 2 V(G) : distT(v0;v) is oddg: Prove that G is bipartite with bipartition fX;Yg. (c) Deduce that a graph is bipartite if and only if it contains no cycles of

2. Determine the Graph Scale a. Determine the magnitude (numeric value) of each variable b. Establish a scale that best fits the range of each variable c. Spread the graph to use the MOST available space (use at least ¾ of the graph) d. Be consistent throughout each axes’ scale 3. Plot the data points a. Plot each data value on the graph ...

Graph theory Multiple Choice Questions(MCQs) with Answers Pdf Free Download for various Interviews, Competitive Exams and Entrance Test like CAT, SAT, MAT, XAT, TANCET, MCA, MBA Exams. - 1

Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. Read each question carefully before you begin answering it. 2. Donʼt spend too long on one question. 3. Attempt every question. 4. Check your answers seem right. 5. Always show your workings ...

Free download in PDF Graph Theory Multiple Choice Questions and Answers for competitive exams. These short objective type questions with answers are very important for Board exams as well as competitive exams. These short solved questions or quizzes are provided by Gkseries.

The graph G[S] = (S;E0) with E0= fuv 2E : u;v 2Sgis called the subgraph induced (or spanned) by the set of vertices S . Graphs derived from a graph Consider a graph G = (V;E). The complement of G, denoted by Gc, is the graph with set of vertices V and set of edges Ec = fuvjuv 62Eg. A graph isomorphic to its complement is called self-complementary.

Solutions Graphtheory - Free download as PDF File (.pdf), Text File (.txt) or read online for free. This document provides solutions to exercises on graph theory: 1) It models several situations as graphs and provides the corresponding adjacency matrices. 2) For given graphs, it determines whether they are planar and bipartite. 3) It draws example graphs matching given properties using Euler's ...

Graph Theory Question 4: Arrange the following graph on the basis of number of edges in increasing order [for n > 3] A. K n (Complete Graph) B. C n (Cycle graph) C. W n (Wheel graph) D. K n, n (Complete Bipartite Graphs) E. Q n (n-cubes graph) Choose the correct answer from the options given below:

Quiz bar graph Data and Graphing Worksheet Eight teams joined a quiz competition. Their final scores are shown below. Study the graph and answer the questions. 0 20 Quiz Points e 1. Which team won the contest? _____ 2. How many points did Team F score? _____ 3. How many more points did Team D get than Team G? _____ 4. Which teams scored equally ...

PRACTICE PROBLEM for Topic 7 – Graphs of sinx, cosx, and tanx 7.1 On a blank sheet of paper, by memory, draw the graphs of sinx, cosx, and tanx on the interval −2π ≤ x ≤ 2π. Label all x and y intercepts, maxima and minima (high and low points), and vertical asymptotes. Answer. See Figures 7.1, 7.2, and 7.3. II. Graphing by Transformations