Assume a graph G is simple (ie. no self loop or parallel edges). Let v be any vertex in the graph. Let boolean[] marked be initalized to all false. Consider: boolean dfs(Graph G, int v) { } marked[v]= true; for (int w G.adj(v)) { if (w == u) continue; if (marked[w]) return true; if (dfs (G, v, w)) return true; } return false; If the call dfs(v) returns true, then: a. The graph has cycles b. The graph is bipartite c. The graph is connected Not enough information b a

Assume a graph G is simple (ie. no self loop or parallel edges). Let v be any vertex in the graph. Let boolean[] marked be initalized to all false. Consider: boolean dfs(Graph G, int v) { } marked[v]= true; for (int w G.adj(v)) { if (w == u) continue; if (marked[w]) return true; if (dfs (G, v, w)) return true; } return false; If the call dfs(v) returns true, then: a. The graph has cycles b. The graph is bipartite c. The graph is connected Not enough information b a

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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*Discrete Math In the graph above, let ε = {2, 3}, Let G−ε be the graph that is obtained from G by deleting the edge {2,3}. Let G∗ be the graph that is obtain from G − ε by merging 2 and 3 into a single vertex w. (As in the notes, v is adjacent to w in the new if and only if either {2,v} or {3,v is an edge of G.) (a) Draw G − ε and calculate its chromatic polynomial. (b) Give an example of a vertex coloring that is proper for G − ε, but not for G. (c) Explain, in own words, why no coloring can be proper for G but not proper for G − ε. (d) Draw G∗ and calculate its chromatic polynomial. (e) Verify that, for this example,PG(k) = PG−ε(k) − PG∗ (k).
Assume a graph G is simple (ie. no self loop or parallel edges) .Let v be any vertex in the graph. Let boolean[] marked be initalized to all false. Consider: boolean dfs(Graph G, int v) { marked[v] = true; for (int w : G.adj(v)) { if (w == u) continue; if (marked[w]) return true; if (dfs (G, v, w)) return true; } return false; } If the call dfs(v) returns true, then: a. The graph has cyclesb. The graph is bipartitec. The graph is connected
1. Input: An unweighted graph G = (V, E).2. Output: C = {C1,C2,...,Ck }, k clusters of G.3. Calculate edge betweenness value ∀(u, v) ∈ E.4. Remove all edges from G that have a higher betweenness value than a threshold τ .5. Find the components of GN which are the clusters of G.Write Python Implementation considering figure
1. Let Sn denote a directed graph with n vertices, numbered from 1 to n, in which there are edges from vertex 1 to all other vertices, and from all other vertices back to vertex 1, but no other edges. Write the Python adjacency list representation for S6.
2. Use the following description of an undirected graph and draw the graph: v(Graph1) = { A, B, C, D} E(Graph1) = { (A,B), (A,D), (B,C), (B,D) }
Alert dont submit AI generated answer. Write a program that reads a weighted graph and an initial vertex.The program must print on the screen the minimum paths obtained by Dijkstra's algorithm. Input: Receives n, m and s; n is the total number of vertices, m the total number of arcs and s is the initial vertex.Next, m lines, each line with a trio of integers, corresponding to the beginning and end of the arc, followed by the weight of the arc.(Vertices are identified from 0 to n-1.) Output: Prints the shortest paths obtained by Dijkstra's algorithm. Exemple: Input: 5 10 00 1 100 4 51 2 11 4 22 3 43 2 63 0 74 1 34 2 94 3 2 Output: [0, 8, 9, 7, 5][-1, 4, 1, 4, 0]
Definition: We define a path in a graph to be short if it contains ≤ 100 edges. Note that we are looking at the number of edges, not the number of vertices. The Problem: •INPUT – An unweighted DAG G = (V, E) – Two specific vertices s, t ∈V •OUTPUT: the number of different short paths in G from s to t. You don’t have to output the actual paths; you just have to figure out how many of them there are. Show a dynamic programming algorithm that solves the above problem in O(|E|) time. You only need to write pseudocode, nothing else. NOTE: a reminder that you can assume in this class that all arithmetic operations (multiplication, addition, etc.) take O(1) time, even if the numbers are very big.
Undirected graph is given with the list of edges. Build an adjacency matrix. Print the number of ones in adjacency matrix. Graph can contain multiple edges and loops. Input First line contains number of vertices n. Each of the next line contains one edge. Read the edges till the end of file. Output Build an adjacency matrix. Print the number of ones in adjacency matrix. Sample input 3 1 2 23 22 32 Sample output 5
4 Write the shortest path length from A to every other node of the above in the Graph and the path component. (e.g. Path A to G: length: 3, consist of: A->C->G) 3 2 2 D F 3 A H. G 4.
If there is an Euler path that starts at AA and ends at some other vertex, give it. Otherwise enter DNE.This should be a list of letters, from A to the other vertex: e.g. ACBDEAD (if that were even possible!). Path: Since this is a planar graph, the number of regions - arcs + nodes equals what number?
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. The chromatic number of a graph is the least mumber of colors required to do a coloring of a graph. Example Here in this graph the chromatic number is 3 since we used 3 colors The degree of a vertex v in a graph (without loops) is the number of edges at v. If there are loops at v each loop contributes 2 to the valence of v. A graph is connected if for any pair of vertices u and v one can get from u to v by moving along the edges of the graph. Such routes that move along edges are known by different names: edge progressions, paths, simple paths, walks, trails, circuits, cycles, etc. a. Write down the degree of the 16 vertices in the graph below: 14…
When a vertex Q is connected by an edge to a vertex K, what is the term for the relationship between Q and K? *a) Q and K are "insecure."b) Q and K are "incident."c) Q and K are "adjacent."d) Q and K are "isolated."