Scalar Product Graphs of Modules

Authors

  • M. Nouri Jouybari Department of Mathematics, University of Mazandaran, Babolsar, Iran
  • S. Firouzian Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
  • Y. Talebi Department of Mathematics, University of Mazandaran, Babolsar, Iran
Abstract:

Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of these graphs is weakly perfect.

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Journal title

volume 10  issue Special Issue ( Nonlinear Analysis in Engineering and Sciences)

pages  75- 82

publication date 2019-12-01

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