Let G = (V, E) be a connected, undirected graph. Let A = V, B = V, and f(u) = neighbours of u. Select all that are true. a) f: A→ Bis not a function Ob) f: A B is a function but we cannot always apply the Pigeonhole Principle with this A, B Oc) f: A ab Di B is a function but we cannot always apply the extended Dain ith thi AR

Let G = (V, E) be a connected, undirected graph. Let A = V, B = V, and f(u) = neighbours of u. Select all that are true. a) f: A→ Bis not a function Ob) f: A B is a function but we cannot always apply the Pigeonhole Principle with this A, B Oc) f: A ab Di B is a function but we cannot always apply the extended Dain ith thi AR

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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3. 4. Given a directed acyclic graph G = (V, E) and two vertices s, te V, design an efficient algorithm that computes the number of different directed paths from s to t. Define the incidence matrix B of a directed graph with no self-loop to be an nxm matrix with rows indexed by vertices, column indexed by edges such that Bij = -1 1 0 if edge j leaves vertex i, if edge jenters vertex i, otherwise. Let BT be the transpose of matrix B. Find out what the entries of the n x n matrix BBT stand for.
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I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O(n + m) as stated in the question.
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