A note on co-maximal graphs of commutative rings
Let R be a commutative ring with unity. The co-maximal graph Γ ( R ) is the graph with vertex set R and two vertices a and b are adjacent if R a + R b = R . In this paper, we characterize rings for which the co-maximal graph Γ ( R ) is a line graph of some graph G and determine rings for which Γ ( R...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2018-04-01
|
| Series: | AKCE International Journal of Graphs and Combinatorics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S097286001830063X |
| Summary: | Let R be a commutative ring with unity. The co-maximal graph Γ ( R ) is the graph with vertex set R and two vertices a and b are adjacent if R a + R b = R . In this paper, we characterize rings for which the co-maximal graph Γ ( R ) is a line graph of some graph G and determine rings for which Γ ( R ) is Eulerian or Hamiltonian. We also find the diameter and girth of Γ ( R ) . Keywords: Finite commutative ring, Maximal ideal, Co-maximal graph, Line graph |
|---|---|
| ISSN: | 0972-8600 |