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Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Answer only question nine and it's a applied discrete mathematics question

Transcribed Image Text:7.
8.
9.
10.
Let G be a regular graph with at least one edge. Assume that there
is a way of partitioning the set of vertices of G into two sets X, Y such that this
partition makes G bipartite. Prove that |X| = |Y.
Let G be a regular graph with a vertex of degree 4 and 10 edges. How
many vertices does it have?
Prove that the complement of a regular graph is also regular.
Prove that a bipartite graph on n vertices has a number of edges less
or equal to 2
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- I want this to be considered as a Advanced Math question pls. . Consider a graph G which is a complete bipartite graph. The graph G is defined as K(3,4), meaning it has two sets of vertices, with 3 vertices in one set and 4 in the other. Every vertex in one set is connected to every vertex in the other set, but there are no connections within a set. Calculate the number of edges in graph G. Also, determine if the graph G contains an Euler path or circuit, and justify your answer.arrow_forwardLet u and v be distinct vertices in a connected graph G. There may be several connected subgraphs of G containing u and v. What is the minimum size of a connected subgraph of G containing u and v? Explain your answer.arrow_forwardLet Vn be the set of connected graphs having n edges, vertex set [n], and exactly one cycle. Form a graph Gn whose vertex set is Vn. Include {gn, hn} as an edge of Gn if and only if gn and hn differ by two edges, i.e. you can obtain one from the other by moving a single edge. Tell us anything you can about the graph Gn. For example, (a) How many vertices does it have? (b) Is it regular (i.e. all vertices the same degree)? (c) Is it connected? (d) What is its diameter?arrow_forward
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