The correct statements are: 3-SAT is polynomially reducible to the INDEPENDENT SET language. 3-SAT is polynomially reducible to the VERTEX-COVER language. 3-SAT is polynomially reducible to the EDGE-COVER language. 3-SAT is polynomially reducible to the TSP-DECIDE language.

Q: tecting a cycle in a directed graph using Depth First Traversal imple

A: Lets see the solution.

Q: Given an undirected graph G, and a path P, we want to verify that P is a cycle that contains all…

A: For this problem we need a certificate verifier algorithm to prove polynomial time verification…

Q: Every strongly connected graph is Eulerian. There is a series of lowercase letters (a-z) that…

A: A directed graph is graph, a set of objects that are connected together.

Q: 2. Find the regular expression for the following Finite Automaton. For this you are requested to…

A: Regular expression for the finite automaton

Q: in C language implement a smallest last ordering for the vertices in a graph

A: Code:-   int smallest_last_ordering(int n, int m, int *U, int *V, int *adj) {   int *deg =…

Q: Give a definition of Graph Embedding, Planar Embedding. Is the following graph a planar graph?…

A:

Q: Give an example of a simple connected graphGfor whichGis planar, has nosubgraph isomorphic toK4, and…

A: Dear Student, The complete solution along with detailed solution and proving that χ(G) = 4 is given…

Q: 4. Run the Bellman-Ford algorithm on the directed graph given blow, using vertex z as the source. In…

A: please see the next steps for solutions.

Q: Wride code for C implementation for finding the whether an undirected graph is connected or not:

A: C++ code to find the connectivity of undirected graph

Q: Q2.Write a Java program to implement Topological sorting for the given Directed acyclic graph. 2 5 3

A: Given graph is a directed graph which contains 6 vertices 1, 2, 3, 4, 5 and 6. The topological…

Q: Prove that the loop invariant is maintained. (loop-invariant
 & notexit-cond & codeloop ⇒…

A: the loop invariant is maintained. (loop-invariant & notexit-cond & codeloop ⇒…

Q: Write a function that returns true (1) if there is an edge between two vertices u and v in an…

A: Since you are not mentioning the programming language, here we are using C++ to complete the…

Q: Prove that the loop invariant is maintained. (loop-invariant
 & notexit-cond & codeloop ⇒…

A: In this question we have to understand and prove the loop invariant is maintained.  Let's understand…

Q: Question 4 Given a undirected weighted graph G = (E,V). With each spanning tree we associate a…

A: First of all we take the labelled edges of spanning trees, which is the maximum age of the spanning…

Q: Question 2. (a) Give the definition of a tree. Definition. A tree is a graph that ... (b) Give a…

A: A tree is a data structure that is used to store information in a hierarchical way. It consists of…

Q: The correct statements are: 2-SAT is in P but 3-SAT is NP-complete. SHORTEST-PATH is in P but…

A: In the realm of computational complexity theory, NP-complete (Non-deterministic Polynomial-time…

Graph Representation

A graph is a non-linear data structure made up of two components namely, vertices and edges. It is represented by as: