A Generalization of Total Graphs of Modules over Commutative Rings under Multiplicatively Closed Subsets

Authors

  • Ahmad Abbasi University of Guilan
  • Leila Hamidian Jahromi University of Guilan University Campus 2

DOI:

https://doi.org/10.30495/jme.v11i0.587

Keywords:

Total graph, generalization of total graphs

Abstract

Let R be a commutative ring and M be an R-module
with a proper submodule N. A generalization of total graphs, denoted
by T(ΓN H(M)), is introduced and investigated. It is the (undirected)
graph with all elements of M as vertices and for distinct x; y 2 M,
the vertices x; y are adjacent if and only if x + y 2 MH(N) where
MH(N) = fm 2 M : rm 2 N for some r 2 Hg and H is a multiplicatively closed subset of R. In this paper, in addition to studying
some algebraic properties of MH(N), we investigate some graph theoretic properties of two essential subgraphs of T(ΓN H(M)).

Author Biographies

Ahmad Abbasi, University of Guilan

Associate professor,

Department of pure mathematics,

Faculty of mathematical sciences,

University of Guilan.

Leila Hamidian Jahromi, University of Guilan University Campus 2

PhD candidate

Department of pure mathematics,

Faculty of mathematical sciences,

University of Guilan.

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Published

2017-08-02

Issue

Vol. 11

Section

Vol. 11, No. 3, (2017)

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