On the graph of modules over commutative rings II | Zendy

H. Ansari-Toroghy | Zendy; Shokoufeh Habibi | Zendy; Masoomeh Hezarjaribi | Zendy

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On the graph of modules over commutative rings II

Author(s) -

H. Ansari-Toroghy,

Shokoufeh Habibi,

Masoomeh Hezarjaribi

Publication year - 2018

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1810657a

Subject(s) - mathematics , commutative ring , bipartite graph , graph , combinatorics , commutative property , discrete mathematics , edge transitive graph , voltage graph , topology (electrical circuits) , line graph

Let M be a module over a commutative ring R. In this paper, we continue our study about the quasi-Zariski topology-graph G(?*T) which was introduced in (On the graph of modules over commutative rings, Rocky Mountain J. Math. 46(3) (2016), 1-19). For a non-empty subset T of Spec(M), we obtain useful characterizations for those modules M for which G(?*T) is a bipartite graph. Also, we prove that if G(?*T) is a tree, then G(?*T) is a star graph. Moreover, we study coloring of quasi-Zariski topology-graphs and investigate the interplay between ?(G(?+T)) and ?(G(?+T)).

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