An exposition on Eulerian irregularity in graphs

• Main Authors: Cheng, Janelle C., Mijares, Nicole G.
• Format: text
• Language: English
• Published: Animo Repository 2015
• Subjects: Graph theory; Domination (Graph theory); Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/18388
• Institution: De La Salle University

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.