   Chapter 10.4, Problem 27ES ### 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
1 views

# A circuit-free graph has ten vertices and nine edges. Is it connected? Why?

To determine

To check:

Whether a circuit free graph, having ten vertices and nine edges, is connected or not.

Explanation

Given information:

Graph with 10 vertices  and 9 edges.

Concept used:

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

Calculation:

Suppose G is a circuit free graph with ten vertices and nine edges.

Let G1,G2,.....,Gk be the connected components of G.

To show that G is connected, we will show that k=1.

Each Gi is a tree since each Gi has ni vertices.

Note that since G has ten vertices in all,

n1+n2+......+nk=10

Since for any positive integer n, any tree with n vertices has n1 edges, we have G1 and n11 edges, G2 has n21 edges,

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