Graph Theory: Let S be a set of three pairwise-nonadjacent edges
in a 3-connected graph G. Show that there is a cycle in G
containing all three edges of S unless S is an edge-cut of G
Draw a 1). position graph, 2). velocity graph, and 3). acceleration
graph of a person standing one second, then goes down into a squat
for three seconds, back up for one second and then a one second
stand for the first rep.
2nd rep- this person goes back down for three seconds, and
then has a one second pause at the bottom of the squat, and then
back up for one second.
2. Draw a graph of the labor market that shows the impact of
reduction in labor demand for two cases (a) wages are perfectly
flexible, and (b) wages are perfectly inflexible (do not change).
Show what happens to labor hours in both cases, and to wage in both
cases. Label everything clearly.
Find the volume of the parallelepiped with adjacent edges
PQ, PR, PS.
P(3, 0, 2), Q(−1, 2,
7), R(4, 2, −1), S(0,
5, 3)
Cubic units
If a = (2, −1, 5)
and b = (4, 2, 1),
find the following.
a × b =
b × a=
If
a = i − 5k and b = j + k, find a × b
1. Prove that for any graph, the sum the degreesPv∈V
deg(v) is twice the number of edges |E|. (By “prove” I mean write a
few sentences explaining why it is true.)
2. i) At a recent math seminar, 5 mathematicians greeted each
other by shaking hands. Is it possible for each mathematician to
shake hands with exactly 3 other people? (No one can shake his or
her own hand.) To answer the question, please rephrase the problem
as a problem about...
-Write a program in C++:
• to find the sum of the series 1! /1+2! /2+3! /3+4! /4+5! /5
using the function1,
• to convert decimal number to binary number using the
function2,
• to check whether a number is a prime number or not using the
function3,
• to check whether two given strings are an anagram using the
function4.
important must do in (Multi-Filing) of c++
Consider an undirected graph G that has n distinct
vertices. Assume n≥3.
How many distinct edges will there be in any circuit for G that
contains all the vertices in G?
What is the maximum degree that any vertex in G can have?
What is the maximum number of distinct edges G can have?
What is the maximum number of distinct edges that G can have if
G is disconnected?
Question 1: Given a graph with length l(e) on edges, find a
minimum length paths from a vertex s to V −s so that among all
shortest lengths paths from s to V −s we find the ones with minimum
number of edges.
Use Dijkstra's algorithm