Intersection graph of a module

Ergün Yaraneri*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

Let V be a left R-module where R is a (not necessarily commutative) ring with unit. The intersection graph {G}(V) of proper R-submodules of V is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper R-submodules of V, and there is an edge between two distinct vertices U and W if and only if U ∩ W ≠ 0. We study these graphs to relate the combinatorial properties of {G}(V) to the algebraic properties of the R-module V. We study connectedness, domination, finiteness, coloring, and planarity for {G} (V). For instance, we find the domination number of {G} (V). We also find the chromatic number of {G}(V) in some cases. Furthermore, we study cycles in {G}(V), and complete subgraphs in {G} (V) determining the structure of V for which {G}(V) is planar.

Original languageEnglish
Article number1250218
JournalJournal of Algebra and its Applications
Volume12
Issue number5
DOIs
Publication statusPublished - Aug 2013

Keywords

  • chromatic number
  • component
  • domination number
  • Intersection graph
  • number of submodules
  • planarity
  • submodule

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