Purchase Solution

graph theory

Not what you're looking for?

Ask Custom Question

Let G be a simple graph on n (greater or equal then) 3 vertices such that deg_G(v) (greater or equal to) n/2 for every vertex v E V(G). Prove that deleting any vertex of G results in a connected graph (i.e. G is 2-connected).

Attachments
Purchase this Solution
Solution Summary

This solution helps prove that deleting any vertex of G results in a connected graph.

Solution Preview

Please see the more readable attached PDF version (Solution.pdf) of the solution below, if possible.

Theorem:
Let G be a simple graph on n >= 3 vertices such that deg_G(v) >= n/2 for every vertex v in V(G). Then deleting any vertex of G results in a connected graph.

Proof:
Let G be a simple connected graph on n >= 3 vertices, and suppose G has a vertex v such that removing v from G results in a disconnected graph (namely, G - {v} -- ...

Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Supply, Demand and their Determinants

    There is also a brief discussion of the efficient markets theory, as well as a graph included.

  • Graph Theory and Parse Tree

    This solution offers to-the-point answers to some assorted questions on graph theory and parse tree.

  • Matching problem

    By a theorem from Graph Theory: every k-regular bipartite graph is 1-factorable, in other words, the edge set E(G) can be partioned into disjoint perfect matchings.

  • indifference theory, budget line and rational choices

    The graph and tables may not print here. Thanks Supposedly, indifference theory can explain all rational choices and behavior ...try the theory out on this situation. Suppose the only consideration for couples to have a baby or not was money.

  • IOS/MCCGraph

    Based on the residual theory, what should be the dollar amount of the total dividend? In the residual theory, all net income is paid as dividends after meeting the capital requirements. Here the requirement of equity is 4.8 million.

  • Graph Theory -Tree and Tree Structures

    Reference: www.wikipedia.com This solution is comprised of a detailed discussion and explanation of the various aspects of Tree and Tree Structures in Graph Theory.

  • Graph Theory : Determine the cycle ranks of Kp, K(m,n) and a connected cubic graph with p vertices.

    148434 Graph Theory : Determine the cycle ranks of Kp Determine the cycle ranks of Kp, K(m,n) and a connected cubic graph with p vertices.

  • Economics - Monetary Theory/Policy

    210899 Economics - Monetary Theory/Policy The graph below shows the demand schedule for a group of students ...(Please see attached file). Option (B) is the answer (Because Consumer Surplus = Area under the Demand Curve but above the Price Line).

  • Graph theory

    13861 Graph Theory. Show that it is impossible for an odd number of people in a group to each know exactly 2k+1 other people in the group for any integer k. Let r be the number of people in the group.

  • Explanations for Discrete Structures problems

    Some problems in graph theory are discussed as well.

View More Related Solutions