Use Big O notation to create witnesses C and K, s f(x) = 3x2 + 25 is O(x²) Also, create a graph in Python which shows "K"
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- Write a java program that takes a matrix representing an undirected graph (connectivity matrix) and finds the minimum spanning tree (using kruskal's or prim's algo.) of that graph and then print it graphically ( Graphical user interface should be used)Using the networkx library of Python, write down the different scripts to draw the following two undirected graphs with labels and complete the following tasks for both the graphs.In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. in its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring.", Wikipedia a) Apply your algorithm in the graph below. What is the accuracy ratio? b) Show that the performance ratio of your algorithm can go unbounded above or never at all.
- Implement the Dijkstra's Algorithm in PYTHON for the given graph. Show the complete source code (text format: can be copied) and screenshot/s of the running output. NOTE: I don't know what's wrong with my code so please help me correct it. # Return the minimum value and index in dist but not in S.def min (G , dist , S) : n = len (G) mdist = float (' inf ')# Find a minimum value. for v in range (n) : if v not in S: if dist [v] < mdist : mdist = dist [v]# Find the first index corresponding to that value. mi = None for v in range (n) : if (v not in S) and (dist [v] == mdist) : mvertex = v break return (mvertex) def dijkstra(G,u) : n = len (G) dist = [float (' inf ' ) ] * n pred = [None] * n s = [] dist [ul] = 0 print ('S : ' + str(S)) print (' dist : ' + str(dist)) while len(S) != n: print (' ') x = min (G, dist , S) print(' Vertex not in S with minimum…make me a graph representation of this code make it in canva/or draw.io only need a screenshot of the graph graph = { 'S': {'U': 1, 'B': 3, 'T':1}, 'U': {'S': 2}, 'B': {'U': 4, 'T':8, 'S':5, 'A':7}, 'T': {'S':2, 'B':6, 'D':2}, 'D': {'B':7, 'A':2, 'C':4}, 'A': {'U':9, 'B':3, 'D':6}, 'C': {'A':8, 'D':5},Write an FSM that accepts those binary numbers with their number of 1s being multiples of three, e.g., 1010100, and 11100111 (but not 1010, nor 001). Draw a graph of your machine and write the formal definition (S, Σ, δ, s0, F).
- Using tables, find the sum of products of expansions of the following Boolean functions. F (x, y, z) = (x +y + z)’y F (x, y, z) = (x +y) +(xy) Draw graph(G) of the following values. G= (V, E) where V = {a, b, c, d} and E = {{a, b}, {a, c},{b,a},{c,a} {b, c},{c,b} {c, d},{d,c}} Find the degree of vertex of the above graph.Programming with Python: v Implement Depth First Search (Traversal) v Implement Breadth First Traversal For the implementation: 1. Create a directed graph with 10 Vertices 2. Add arbitrary edges among vertices to satisfy the directed graph 3. Run your program and show appropriate output (Traversal order) 4. Your implementation should be fully commented Please, submit your source code and output (Screen Capture) too.Suppose you have a graph G with 6 vertices and 7 edges, and you are given the following information: The degree of vertex 1 is 3. The degree of vertex 2 is 4. The degree of vertex 3 is 2. The degree of vertex 4 is 3. The degree of vertex 5 is 2. The degree of vertex 6 is 2. What is the minimum possible number of cycles in the graph G?
- (1)In a graph, the sum of the degrees of all vertices is equal to () times the number of edges of the graph. A．1/2 B．1 C．2 D．4 (2) In a directed graph, the sum of the in degrees of all vertices is equal to () times the sum of the out degrees of all vertices. A．1/2 B．1 C．2 D．4 (3) A directed graph with n vertices can have at most () edges. A．n B．n(n-1) C．n(n+1) D．n2 (4) When a connected graph with n vertices is represented by an adjacent distance matrix, the distance matrix has at least () nonzero elements. A．n B．2(n-1) C．n/2 D．n2 (5) G is a disconnected undirected graph with 28 edges, then the graph has at least () vertices. A．7 B．8 C．9 D．10Write a program, in C language, that will do the following: It will show if all the nodes are connected to the graph or not. Given a graph check that it is isomorphic (all nodes and all edges and weights are the same). We are given a graph with non-negative weights (produce them randomly) in which we have randomly colored the edges as red or blue. For each node, find the minimum cost of moving from a source node with the help of a path that has at least one red edge. It will accept a graph and show if it is undirected (if there are directed edges in both directions for all nodes connected to each other).6. In Java create an algorithm for an undirected graph with n vertices and m edges that...- Takes as a parameter some integer k- Returns the maximum induced subgraph where each vertex of that subgraph has a degree greater than or equal to k (or returns null if no such subgraph exists)- Operates in O(n + m) time