A graph equation between the line graph and the edge-complement graph
| Autor: | Senja Barthel, Fabio Buccoliero |
|---|---|
| Přispěvatelé: | Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Barthel, S & Buccoliero, F 2021, A graph equation between the line graph and the edge-complement graph . in Proceedings of the 3rd BYMAT Conference : Vol 2 . vol. 2, TEMat monográficos, Asociación Nacional de Estudiantes de Matemáticas (ANEM), pp. 231-234 . < https://temat.es/monograficos/article/view/vol2-p231 > Vrije Universiteit Amsterdam Proceedings of the 3rd BYMAT Conference: Vol 2, 2, 231-234 |
| Popis: | From a graph G related graphs can be constructed, such as its line graph L(G) and its edge-complement graph \bar{G}. After showing how properties of G imply properties of L(G), we ask how different the concepts of the line graph and that of the edge-complement graph are, by solving the equation L(G)≃\bar{G}. We show that the equation has only two solutions. The proof uses an argument on the degree of the vertices of a graph that allows to reduce the number of possible solutions until they can be checked algorithmically. This gives an alternative proof to the one by Aigner. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|