Question 1. Design vertices of the lower case k. 2. What is the adjacency matrix? 3. Using Python program to draw the lower case k. 4. Rotate the lower case k by 45◦counterclockwise. 5. Draw the backward lower case k. The lower case letter k is shown in Figure 1. As can be seen, the letter is determined by a set of vertices. In this project, you will use matrices, transformations and Python program to draw different lower case k. k.

Ans 1N = 200005n, m, =0,0vis=[0 for i in range(N)]gr=[[] for i in range(N)]v=[[] for i in range(2)]def add_edges(x, y): gr[x].append(y) gr[y].append(x)def dfs(x, state): v[state].append(x) vis[x] = 1 for i in gr[x]: if (vis[i] == 0): dfs(i, state ^ 1)def Print_vertices(): if (len(v[0]) < len(v[1])): for i in v[0]: print(i,end=" ") # If even level vertices are less else: for i in v[1]: print(i,end=" ")n = 4m = 3add_edges(1, 2)add_edges(2, 3)add_edges(3, 4)dfs(1, 0)Print_vertices()def display(n): v = n while ( v >= 0) : c = 65 for j in range(v + 1): print( chr ( c + j ), end = " ") v = v - 1 print() for i in range(n + 1): c = 65 for j in range( i + 1): print( chr ( c + j), end =" ") print()n = 5display(n)Ans 2The adjacency matrix, also called theconnection matrix, is a matrix containing rows andcolumns which is used to represent a simple labelled graph, with 0or 1 in the position of (Vi , Vj) accordingto the condition whether Vi and Vj areadjacent or not. It is a compact way to represent the finite graphcontaining n vertices of a m x m matrix M. Sometimes adjacencymatrix is also called as vertex matrix and it isdefined in the general form asIf the simple graph has no self-loops, Then the vertex matrixshould have 0s in the diagonal. It is symmetric for the undirectedgraph. The connection matrix is considered as a square array whereeach row represents the out-nodes of a graph and each columnrepresents the in-nodes of a graph. Entry 1 represents that thereis an edge between two nodes.Ans 3def display(n): v = n while ( v >= 0) : c = 65 for j in range(v + 1): print( chr ( c + j ), end = " ") v = v - 1 print() for i in range(n + 1): c = 65 for j in range( i + 1): print( chr ( c + j), end =" ") print()n = 5display(n)Ans 4import imutilstext = cv2.imread("k")Rotated_text = imutils.rotate(text, angle=45)cv2.imshow("Rotated", Rotated_text)cv2.waitKey(0)Ans 5s=input()new_str="k"for i in range (len(s)): if s[i].isupper(): new_str+=s[i].lower() elif s[i].islower(): new_str+=s[i].upper() else: new_str+=s[i]print(new_str) ...