1. Consider the directed acyclic graph (DAG) D shown below.(a) Write down the adjacency matrix A corresponding to the ordering of the verticesgiven by alphabetical order: a, b, c, d, e, f, g.(b) Find all permutations of the set of vertices {a, b, c, d, e, ƒ, g} such that the asso-ciated adjacency matrix is strictly lower triangular.(c) Find the number of spanning trees rooted at vertex g.

Adjacency Matrix Representation: If a directed graph G consists of n vertices then the adjacency…

Answered: 1. Consider the directed acyclic graph…

1. Consider the directed acyclic graph (DAG) D shown below. (a) Write down the adjacency matrix A corresponding to the ordering of the vertices given by alphabetical order: a, b, c, d, e, f, g.

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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Question

1. Consider the directed acyclic graph (DAG) D shown below.
(a) Write down the adjacency matrix A corresponding to the ordering of the vertices
given by alphabetical order: a, b, c, d, e, f, g.
(b) Find all permutations of the set of vertices {a, b, c, d, e, ƒ, g} such that the asso-
ciated adjacency matrix is strictly lower triangular.
(c) Find the number of spanning trees rooted at vertex g.

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