Question

2.21 Recall that a graph G is regular if each vertex has the same degree. Suppose G is a connected regular graph with n vertices and $n \ge 3$. (a) Prove that G must be eulerian if n is odd. (b) Give examples to demonstrate that if n is even then G may or may not be eulerian.

          2.21 Recall that a graph G is regular if each vertex has the same degree. Suppose G is a connected regular graph with n vertices and $n \ge 3$.
(a) Prove that G must be eulerian if n is odd.
(b) Give examples to demonstrate that if n is even then G may or may not be eulerian.

2.21 Recall that a graph G is regular if each vertex has the same degree. Suppose G is a connected regular graph with n vertices and n ≥ 3.
(a) Prove that G must be eulerian if n is odd.
(b) Give examples to demonstrate that if n is even then G may or may not be eulerian.

Added by Joshua M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Mahajan A

02/28/2022

Step 1

Since G has n vertices, the sum of the degrees of all vertices in G is nd. Show more…

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2.21 Recall that a graph G is regular if each vertex has the same degree. Suppose G is a connected regular graph with n vertices and n ≥ 3. (a) Prove that G must be eulerian if n is odd. (b) Give examples to demonstrate that if n is even then G may or may not be eulerian.