   Chapter 10.4, Problem 26ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# If a graph has n vertices and n − 2 or fewer can it be connected? Why?

To determine

To check:

Whether a graph, having n vertices and n-2 or fewer edges, is connected or not.

Explanation

Given information:

Graph with n vertices  and n2 or fewer edges.

Concept used:

Any tree with n vertices has n1 edges and total degree is 2(n1).

Calculation:

Claim: such a graph cannot be connected.

Reason: if possible suppose that the graph is connected then the graph or any of its sub graph with all the vertices can be a tree because a graph and all of its sub graph with n vertices has edges fewer than n1

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