Nilpotent graphs with crosscap at most two
Let be a commutative ring with identity. The nilpotent graph of , denoted by , is a graph with vertex set , and two vertices and are adjacent if and only if is nilpotent, where . In this paper, we characterize finite rings (up to isomorphism) with identity whose nilpotent graphs can be embedded in t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2018-12-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2017.11.006 |
| Summary: | Let be a commutative ring with identity. The nilpotent graph of , denoted by , is a graph with vertex set , and two vertices and are adjacent if and only if is nilpotent, where . In this paper, we characterize finite rings (up to isomorphism) with identity whose nilpotent graphs can be embedded in the projective plane or Klein bottle. Also, we classify finite rings whose nilpotent graphs are ring graph or outerplanarity index 1,2. |
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| ISSN: | 0972-8600 |