Open AccessOn 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)).