An exposition on Eulerian irregularity in graphs
In this paper, we present an exposition of the first two sections in the article, On Eulerian Irregularity in Graphs . In the Chinese Postman Problem, we are asked to find the minimum length of a closed walk in a connected graph G such that every edge of G appears on the walk once or twice. Another...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
2015
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/18388 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | In this paper, we present an exposition of the first two sections in the article, On Eulerian Irregularity in Graphs . In the Chinese Postman Problem, we are asked to find the minimum length of a closed walk in a connected graph G such that every edge of G appears on the walk once or twice. Another interesting problem is finding the minimum length of a closed walk in G in which no two edges are encountered the same number of times. An Irregular Eulerian Walk in G is an Eulerian Walk that encounters no two edges of G the same number of times. The minimum length of an Irregular Eulerian Walk in G is said to be the Eulerian Irregularity of G, denoted by EI(G). Given a nontrivial connected graph G of size m, we determine the minimum length of an Irregular Eulerian walk in G known as the Eulerian Irregularity of G such that m + 1 2 EI(G) 2 m + 1 2 : 1. |
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