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Transcribe in digital format the following text

Transcribe in digital format the following text

Database System Concepts
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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NOW, (P₁-1) + (P₂-1) = P₁ + R₂-2 = P-2 (P₁−1)²+(1₂-1)² + 2 (P-1) (P₂-1) = (P-2)² [Squaring bort sides] → (P₁-1) ² + (₁₂-1) ² ≤ (P-2) ² [22 (1₁-1) (12-1) > 0] → P₁² + P₂² - 2 (P₁+P₂) + 2 ≤ p²-4P+4 = = P₁² + P₂² ≤ p²-2p+2 So, the maximus no. [²² P₁+₁₂=P] of edges in G = ²/²/2 [ P₁² + P₂²² -P] ≤ But, given that, p²3p+2 2 2 (P-1) (P-2) 2 G has more than (P-1) (P-2) edges. 15ms, We get a contradiction. so, our assumption is wrong. Hence, G is connected (Prove)
Transcribed Image Text:NOW, (P₁-1) + (P₂-1) = P₁ + R₂-2 = P-2 (P₁−1)²+(1₂-1)² + 2 (P-1) (P₂-1) = (P-2)² [Squaring bort sides] → (P₁-1) ² + (₁₂-1) ² ≤ (P-2) ² [22 (1₁-1) (12-1) > 0] → P₁² + P₂² - 2 (P₁+P₂) + 2 ≤ p²-4P+4 = = P₁² + P₂² ≤ p²-2p+2 So, the maximus no. [²² P₁+₁₂=P] of edges in G = ²/²/2 [ P₁² + P₂²² -P] ≤ But, given that, p²3p+2 2 2 (P-1) (P-2) 2 G has more than (P-1) (P-2) edges. 15ms, We get a contradiction. so, our assumption is wrong. Hence, G is connected (Prove)
9 Given that, G is a graph of Orden p and his size greaten than (P-1) (P-1) (P-2) = 2 2 we have to show, Then The result is true orily when G is Simple graph Now, Let us assume that G is not connected. G has at least two Connected Components. Say G₁ G₂ 9 Suppose, then, P+P₂=P as the graph is simple, and The maximum Then G is connected. The Order of the Рід P2 graph G₁9 G₂ are P₁ 3 Pz respectively so both G₁ 9. G₂ are Simple. of edges in Gi is PiCz Pi (Pi-1) 2 + no of edges = so, the maximum sio. of edges in G P₁ (P₁-1) P2 (P₂-1). 2 2 ; 1=1,2 = = [₁²³+R² = (₁+B₂)] = { [9²6²³=P] -
Transcribed Image Text:9 Given that, G is a graph of Orden p and his size greaten than (P-1) (P-1) (P-2) = 2 2 we have to show, Then The result is true orily when G is Simple graph Now, Let us assume that G is not connected. G has at least two Connected Components. Say G₁ G₂ 9 Suppose, then, P+P₂=P as the graph is simple, and The maximum Then G is connected. The Order of the Рід P2 graph G₁9 G₂ are P₁ 3 Pz respectively so both G₁ 9. G₂ are Simple. of edges in Gi is PiCz Pi (Pi-1) 2 + no of edges = so, the maximum sio. of edges in G P₁ (P₁-1) P2 (P₂-1). 2 2 ; 1=1,2 = = [₁²³+R² = (₁+B₂)] = { [9²6²³=P] -
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