Some Results of the Normal Intersection Graph of a Group

Authors

  • Ali Iranmanesh Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-137, Tehran
  • Elham Aboomahigir Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-137, Tehran

DOI:

https://doi.org/10.26713/cma.v9i2.645

Keywords:

Group, Normal intersection graph, Planar

Abstract

Let \(G\) be a group. We denote the normal intersection graph of subgroups of \(G\) by \(\Delta(G)\), and define it as an undirected graph with no loops and multiple edges, whose vertex set is the set of all non-trivial subgroups of \(G\) and two distinct vertices \(H\) and \(K\) are adjacent if and only if \(H\cap K\) is normal in \(G\). In this paper, we characterize all of groups \(G\) whose the normal intersection graph of \(G\) is planar and we investigate some other properties of this graph.

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References

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Published

30-06-2018
CITATION

How to Cite

Iranmanesh, A., & Aboomahigir, E. (2018). Some Results of the Normal Intersection Graph of a Group. Communications in Mathematics and Applications, 9(2), 127–137. https://doi.org/10.26713/cma.v9i2.645

Issue

Vol. 9 No. 2 (2018)

Section

Research Article

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