都市主义代写 Urbanism代写 Assignment代写 作业课业代写
1089Urbanism Assignment #3 – Reconceiving the public realm 都市主义代写 Throughout the semester we have been studying various urban types and design proposals that have emerged as the result of ...
View detailsSearch the whole station
图论代写 This assignment forms 5% of the assessment for this module. The assignment will be marked out of 20 marks. Please answer all questions,
This assignment forms 5% of the assessment for this module.
The assignment will be marked out of 20 marks.
Please answer all questions, fully justifying your answers. Think about your mathematical style – the aim is for clear, streamlined solutions. Good choice of notation can help clarify your arguments. You may cite results from the notes without proof.
• for each edge e of G, create a vertex ve of G’ ;
• two vertices ve1 , ve2 of V (G’ ) are joined by an edge in G’ if and only if the corresponding edges e1, e2 of E(G) share an endpoint in G.
In other words, G’ has vertices in one-to-one correspondence with the edges of G, and two vertices are adjacent in G’ precisely if the corresponding edges are adjacent in G. For example,
(i) Let Pn denote the path on n vertices (n ≥ 2). Prove that P’n is isomorphic to Pn−1.
(ii) There exists an infinite family of graphs Gn (n ≥ 2) such that
G’n ≌ Kn−1
where Kn−1 is the complete graph on n − 1 vertices.
Give the vertex set and edge set of such a family, and prove that it has the stated property. (4 marks)
Let G be a graph.
(i) Prove that if G is connected then G’ is connected.
(ii) If G’ is connected, is G necessarily connected? Prove or give a counterexample. (5 marks)
Let G be a graph. Write down a formula expressing the degree of a vertex vxy ∈ V (G’ ), in terms of the degree of x, y ∈ V (G). (2 marks)
Prove that if a graph G is Eulerian, then G’ is Eulerian. (2 marks)
Is it true that if a graph G is connected and G’ is Eulerian, then G is Eulerian? Prove or give a counterexample. (2 marks)
Let G be a graph on n vertices {1, . . . , n}, where deg i = di . Prove that
更多代写:Python网课托管推荐 GMAT代考 英国数量分析代上网课 商科essay论文 商业论文写作方法指导 代写EMBA论文
Urbanism Assignment #3 – Reconceiving the public realm 都市主义代写 Throughout the semester we have been studying various urban types and design proposals that have emerged as the result of ...
View detailsCS420/520: Graph Theory with Applications to CS, Winter 2022 Homework 2 CS算法代写 Homework Policy: 1. Students should work on homework assignments in groups of preferably three people. Eac...
View detailsMT5863 Semigroup theory: Problem sheet 3 半群理论作业代做 Binary relations and equivalences 3-1. Let X = {1, 2, 3, 4, 5, 6}, let ρ be the equivalence relation on X with equivalence classes {1,...
View detailsHomework 3 数学统计作业代写 Instructions: Solve the problems in the spaces provided and save as a single PDF. Then upload the PDF to Canvas Assignments by the due date. Instructions: Solve t...
View details