1- Compare the required space for graph representation in terms of edges and vertices usinga) list of edges, b) adjacency matrix, and adjacency list2- Explain the Adjacency-list graph representation codepublic class Graph{private final int V;private Bag[] adj;public Graph(int V){this.V = V;adj(Bag[]) new Bag[V];for (int v = 0; v < V; v++)adj[v]= new Bag();}public void addEdge (int v, int w){adj[v].add(w);adj[w].add(v);}public Iterable adj(int v){ return adj[v]; }}

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1- Compare the required space for graph representation in terms of edges and vertices using a) list of edges, b) adjacency matrix, and adjacency list

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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(a) Let G be a simple undirected graph with 18 vertices and 53 edges such that the degreesof G are only 3 and 7. Suppose there are a vertices of degree 7 and b vertices ofdegree 3. Find a and b. To receive any credit for this problem you must write completesentences, explain all of your work, and not leave out any details. problem 1, continued(b) Recall that a graph G is said to be k-regular if and only if every vertex in G has degreek. Draw all 3-regular simple graphs with 12 edges (mutually non-isomorphic). Hint:there are six of them. To receive credit for this problem, you should explain, as well aspossible, why all of your graphs are mutually non-isomorphic.
1- Create a struct to store the node label and its cost:struct Node{char label;int cost;};SCS214: Data StructuresAssignment-42- Implement a class MinHeap that has the following declaration:3- Create a class WeightedGraph, which stores a graph using an adjacency matrixwith the following declaration:class WeightedGraph{ int** g; int nVertices;public:int getNVertices();//returns the number of vertices int getWeight(char,char);//returns weight of the edge connecting the givenvertices int* returnNeighbors(int v);// returns the indices of the neighbors of the vertexv as an int array int numNeighbors(int v);//returns the number of neighbors of the vertex v void loadGraphFromFile(ifstream&);//allocates the adjacency matrix & initializesedge weights from the specified file void dijkstra(char startVertex, char* prev, Node distances[] );//find the shortestpath from the start vertex to all other vertices, by filling the prev array and thedistances array};class MinHeap{ Node* heap; //an…
16.15 It is a fairly common practice to traverse the vertices and edges of agraph. Consider a new implementation of graphs that keeps a Map of verticesas well as an unordered List of edges. This makes traversal of edges simple.What is the complexity of each of the other Graph operations?16.16 Extend the all-pairs minimum distance algorithm to keep track of theshortest path between the nodes.16.17 Explain why it is sometimes more efficient to compute the distancefrom a single source to all other nodes, even though a particular query may beanswered with a partial solution.
DATA STRUCTURES AND ALGORITHMS C++ Write an algorithm which provides a path from a specific source to destination node in a graph withminimum stops. Draw a directed graph from the following adjacency list. Simulate/dry run your algorithm on it and provide step-by-step updates of values in used data structure(s) considering “A” as source and “J” asdestination.
DAG's LCA. Get the lowest common ancestor (LCA) of v and w given a DAG and two vertices, v and w. The LCA of v and w is an ancestor of v and w who has no offspring who are likewise v and w's ancestors. Finding the degree of inbreeding in a pedigree graph and other applications involving genealogical data analysis and multiple inheritance in computer languages both benefit from computing the LCA. Hint: In a DAG, define the height of a vertex as the distance along the longest path from a root to the vertex. An LCA of v and w has the highest height among vertices that are both ancestors of v and w.
Graphs 1- Compare the required space for graph representation in terms of edges and vertices using a) list of edges, b) adjacency matrix, and adjacency list 2- Explain the Adjacency-list graph representation code…
1. Using the graph below, a. Draw an adjacency list and matrix. b. Perform a depth first search using Vertex C as your source draw the resulting depth first search tree.
Graph ColoringNote that χ(G) denotes the chromatic number of graph G, Kndenotes a complete graph on n vertices, and Km,n denotes the complete bipartite graph inwhich the sets that bipartition the vertices have cardinalities m and n, respectively. (c) Compute χ(K3,3). Justify your answer with complete details and complete sentences. (d) For n, m ∈ N, compute χ(Km,n). Do not justify your work. (e) Give an example of a graph G whose chromatic number is 3, but that contains no K3 as a subgraph
problem 22.4-3 on page 615 of the text – Also implement your algorithm. In each case you should have a graph class (graph.h and graph.cpp). You may use either graph implementation.
1 A spanning tree for an undirected graph is a sub-graph which includes all vertices but has no cycles. There can be several spanning trees for a graph. A weighted undirected graph can have several spanning trees One of the spanning trees has smallest sum of all the weights associated with the edges. This tree is called minimum spanning tree (MST). Find the MST in the following graph using Kruskal?s Algorithm. V={a, b, c, d, e, f, g, h, i, j} and E={(a, b, 12), (a, b, 3), (a, j, 13), (b, c, 12), (b, d, 2), (b, h, 4), (b, i, 25), (c, d, 7), (c, j, 5), (e, f, 11), (e, j, 9), (f, g, 15), (f, h, 14), (g, h, 6), (h, d, 20), (h, i, 1) }. Note: Numeric value is the weight of the corresponding edge.
Discussion:1. Depth-first search (DFS) is a technique that is used to traverse a tree or a graph.DSF technique starts with a root node and then traverses the adjacent nodes ofthe root node by going deeper into the graph. In the DFS technique, the nodes aretraversed depth-wise until there are no more children to explore.- Once we reach the leaf node (no more child nodes), the DFS backtracks andstarts with other nodes and carries out traversal n a similar manner. DFStechnique uses a stack data structure to store the nodes that are beingtraversed. DFS Technique (Depth-First Traversal)o Following is the algorithm for the DFS technique.o Algorithm:1. Start with the root node and insert it into the stack2. Pop the item from the stack and insert into the ‘visited’ list3. For the node marked as ‘visited’ (or in visited list), add the adjacent nodesof this node that are not yet marked visited to the stack.4. Repeat steps 2 and 3 until the stack is empty.
please tell me whats wrong with this code/ please fix it ( in C) #include<stdio.h> #include<stdlib.h> #define MAXIMUM 100 #define intial 1 #define waitng 2 #define visiited 3 int n; int adj[MAXIMUM][MAXIMUM]; int state[MAXIMUM]; void create_Graph(); void breadth_First_Search_Traversal(); void breadth_First_Search(int v); int que[MAXIMUM], frnt = -1,rearr = -1; void insert-Queue(int vertex); int delete_Queue(); int is_Empty_Queue(); int main() { create_Graph(); breadth_First_Search_Traversal(); return 0; } void breadth_First_Search_Traversal() { int h; for(h=0; h<n; h++) state[h] = intial; printf("Enter Start Vertex for breadth_First_Search: \n"); scanf("%d", &h); breadth_First_Search(h); } void breadth_First_Search(int h) { int i; insert-Queue(h); state[h] = waitng; while(!is_Empty_Queue()) { h= delete_Queue( ); printf("%d ",h); state[h] =…