23. If a planar drawing of a graph has 15 edges and 8 vertices, how many faces does the graph have?

Construct a graph with vertices A, B, C, D, E whose degrees are 1, 1, 1, 0, 1 What is the edge set?

How many edges does Cn have

For the cube graph , the distance between two vertices a=(a1,a2,...,an) and b=(b1,b2,...,bn) is called the “Hamming distance.”  This is the number of positions where a and b differ.  For instance, the Hamming distance between (0,0,1,0) and (1,1,0,0) is 3 because these two vertices differ in three positions.  In each of the parts A,B below, D(x,y) is the Hamming distance in Qn: B. Show that if D(a,b) and D(b,c) have different parity, then D(a,c) must be odd.

Question 4. Let K, be the complete graph on n vertices. How many edges does it have? Justify your answer.

Construct a graph with vertices J, K, L, M, N whose degrees What is the edge set? "

For the cube graph , the distance between two vertices a=(a1,a2,...,an) and b=(b1,b2,...,bn) is called the “Hamming distance.”  This is the number of positions where a and b differ.  For instance, the Hamming distance between (0,0,1,0) and (1,1,0,0) is 3 because these two vertices differ in three positions.  In each of the parts A,B below, D(x,y) is the Hamming distance in Qn: A. Show that if D(a,b) and D(b,c) have the same parity (i.e., are both even or are both odd), then D(a,c) must be even. B. Show that if D(a,b) and D(b,c) have different parity, then D(a,c) must be odd.

In a high school class, there are students of different talents (ex. music, art, debate, sports, etc.). A committee needs to be formed consisting of the maximum number of students such that the committee is diverse – no two students with the same talent are in the committee. Transform this problem to a graph theoretic problem. What are the vertices of the graph? What are the edges of the graph? What do you have to find in the graph?

The graph with edges AC and BD is a connected graph. True False