The Zariski topology-graph of modules over commutative rings II

Autor: Sh. Habibi, Habibollah Ansari-Toroghy
Rok vydání: 2020
Předmět:
Zdroj: Arabian Journal of Mathematics. 10:41-50
ISSN: 2193-5351
2193-5343
DOI: 10.1007/s40065-020-00301-1
Popis: Let M be a module over a commutative ring R. In this paper, we continue our study about the Zariski topology-graph $$G(\tau _T)$$ G ( τ T ) which was introduced in Ansari-Toroghy et al. (Commun Algebra 42:3283–3296, 2014). For a non-empty subset T of $$\mathrm{Spec}(M)$$ Spec ( M ) , we obtain useful characterizations for those modules M for which $$G(\tau _T)$$ G ( τ T ) is a bipartite graph. Also, we prove that if $$G(\tau _T)$$ G ( τ T ) is a tree, then $$G(\tau _T)$$ G ( τ T ) is a star graph. Moreover, we study coloring of Zariski topology-graphs and investigate the interplay between $$\chi (G(\tau _T))$$ χ ( G ( τ T ) ) and $$\omega (G(\tau _T))$$ ω ( G ( τ T ) ) .
Databáze: OpenAIRE
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