| Autor: |
Andrews Eric, Lumduanhom Chira, Zhang Ping |
| Jazyk: |
angličtina |
| Rok vydání: |
2014 |
| Předmět: |
|
| Zdroj: |
Discussiones Mathematicae Graph Theory, Vol 34, Iss 2, Pp 391-408 (2014) |
| Druh dokumentu: |
article |
| ISSN: |
2083-5892 |
| DOI: |
10.7151/dmgt.1744 |
| Popis: |
A closed walk in a connected graph G that contains every edge of G exactly once is an Eulerian circuit. A graph is Eulerian if it contains an Eulerian circuit. It is well known that a connected graph G is Eulerian if and only if every vertex of G is even. An Eulerian walk in a connected graph G is a closed walk that contains every edge of G at least once, while 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 called the Eulerian irregularity of G and is denoted by EI(G). It is known that if G is a nontrivial connected graph of size m, then . A necessary and sufficient condition has been established for all pairs k,m of positive integers for which there is a nontrivial connected graph G of size m with EI(G) = k. A subgraph F in a graph G is an even subgraph of G if every vertex of F is even. We present a formula for the Eulerian irregularity of a graph in terms of the size of certain even subgraph of the graph. Furthermore, Eulerian irregularities are determined for all graphs of cycle rank 2 and all complete bipartite graphs |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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