| Autor: |
Boro, Laithun, Singh, Madan Mohan |
| Předmět: |
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| Zdroj: |
Discrete Mathematics, Algorithms & Applications; Feb2024, Vol. 16 Issue 2, p1-12, 12p |
| Abstrakt: |
Let R be a commutative ring with unity. Taloukolaei and Sahebi [Von Neumann regular graphs associated with rings, Discrete Math. Algorithms Appl. 10(3) (2018) 1850029, doi:10.1142/S1793830918500295] introduced the Von Neumann regular graph G V n r + (R) of a ring R whose vertices are the elements of R and two distinct vertices x and y are adjacent if and only if x + y is a Von Neumann regular element of R. In this paper, we investigate and determine some graph theoretic properties of the line graph L (G V n r + (R)) associated to G V n r + (R). We give some characterization results regarding the completeness, bipartiteness, traversability, diameter and girth. We also prove Beck's conjecture for L (G V n r + (R)). Finally we characterize rings having the planarity, the outerplanarity and also being the ring graph of the line graphs associated to Von Neumann regular graphs L (G V n r + (R)) of rings. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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