Data Structure: Unit IV : Multiway Search Trees and Graphs

Euler Circuits

Euler path, Operations | Graphs | Data Structure

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In graph theory there is a famous problem known as konigsberg bridge problem. In this problem the main theme was to cross the seven bridges exactly once to visit various cities.

Euler Circuits

In graph theory there is a famous problem known as konigsberg bridge problem. In this problem the main theme was to cross the seven bridges exactly once to visit various cities. The Swiss mathematician Leonhard Euler solved this problem in 1736. From this problem, the concept of Euler circuit is developed. Let us define the terminologies Euler path and Euler circuit.

Euler path A path in a graph G is called Euler path if it includes every edge exactly once and every vertex gets visited. Euler circuit on graph G is an Euler path that visits each vertex of graph G and uses every edge of G.

For example

The Euler circuit is A - B – E – A – D – B – C – E – D - C - A.


Ex. 5.12.1 Find an Euler path or an Euler circuit using DFS for the following graph.

Euler circuit is a circuit that uses every edge of graph exactly once. It starts and ends at the same vertex.

Review Questions

1. Give a short note on euler circuits.

2. Explain euler circuit with an example.

Data Structure: Unit IV : Multiway Search Trees and Graphs : Tag: : Euler path, Operations | Graphs | Data Structure - Euler Circuits

Home | Department: CSE Department | Subject: Data Structure |
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Data Structure: Unit IV : Multiway Search Trees and Graphs


B-Tree - Operations, properties, Algorithm | Data Structure

B+ Tree - Definition, Construction of Example Operations | Data Structure

Graph Definition - with Example | Data Structure

Basic Terminologies in Graph - Data Structure

Representation of Graph - with Example C Programs | Data Structure

Types of Graph - Data Structure

Graph Operations - with Example C Programs | Data Structure

Graph Traversal Methods - Operations, Algorithm with Example C Programs | Data Structure

Topological Sort - Definition, Operations, Algorithm with Example C Programs | Graphs | Data Structure

Bi-Connectivity - Graph Properties, Definition, Operations | Graphs | Data Structure

Cut Vertex - Definition, Operations, Algorithm | Graphs | Data Structure

Euler Circuits - Euler path, Operations | Graphs | Data Structure

Applications of Graphs - Data Structure

Finding Shortest Path - Operations, Algorithm with Example C Programs | Graphs | Data Structure

Minimum Spanning Tree - Operations, Algorithm with Example C Programs | Graphs | Data Structure

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