G1 G2 h (a) Prove that the graphs G1 and G2 are isomorphic by exhibiting an isomorphism from one to the other by concrete arguments and verify it by using adjacency matrices. Please take the ordering of the vertices as a, b, c, d, e, h while forming AG, , adjacency matrix of G1. Warning: One must stick to the labelings of the vertices as they are given, if one changes the labelings/orderings etc., the solution will not be taken into account. (b) Consider the complete graph K17 with vertex set V17 = {u1, u2, Uz, · ,u17}. Let H = (V, E) be the simple graph obtained from K17 by adding a new vertex u, i.e. V = V17 U {u} and deleting the edges {u1, u2} and {u2, uz} and adding the edges {u1, u} and {u, u2} and keeping the remaining edges same. Determine whether H has an Euler circuit or not, an Euler path or not. One must validate any con- clusion by clear arguments.

G1 G2 h (a) Prove that the graphs G1 and G2 are isomorphic by exhibiting an isomorphism from one to the other by concrete arguments and verify it by using adjacency matrices. Please take the ordering of the vertices as a, b, c, d, e, h while forming AG, , adjacency matrix of G1. Warning: One must stick to the labelings of the vertices as they are given, if one changes the labelings/orderings etc., the solution will not be taken into account. (b) Consider the complete graph K17 with vertex set V17 = {u1, u2, Uz, · ,u17}. Let H = (V, E) be the simple graph obtained from K17 by adding a new vertex u, i.e. V = V17 U {u} and deleting the edges {u1, u2} and {u2, uz} and adding the edges {u1, u} and {u, u2} and keeping the remaining edges same. Determine whether H has an Euler circuit or not, an Euler path or not. One must validate any con- clusion by clear arguments.

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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