Let $R$ be a finite local ring of characteristic a power of $2$ with the residue field $k$. In this paper, we define a generalized orthogonal graph on a module of rank at least $2$ over $R$. Then we study its graph properties via the same graph over $k$. The number of vertices and the valency of each vertex in this graph over $R$ are computed. We also prove that this graph is arc transitive and find its diameter. Moreover, the first subconstituent of this orthogonal graph is considered. We show that it is a generalized strongly regular graph.
Sriwongsa, S., & Wei, Y. (2022). Generalized orthogonal graphs of characteristic a power of 2. Journal of Algebra and Related Topics, 10(1), 51-61. doi: 10.22124/jart.2021.20476.1310
MLA
S. Sriwongsa; Y. Wei. "Generalized orthogonal graphs of characteristic a power of 2". Journal of Algebra and Related Topics, 10, 1, 2022, 51-61. doi: 10.22124/jart.2021.20476.1310
HARVARD
Sriwongsa, S., Wei, Y. (2022). 'Generalized orthogonal graphs of characteristic a power of 2', Journal of Algebra and Related Topics, 10(1), pp. 51-61. doi: 10.22124/jart.2021.20476.1310
VANCOUVER
Sriwongsa, S., Wei, Y. Generalized orthogonal graphs of characteristic a power of 2. Journal of Algebra and Related Topics, 2022; 10(1): 51-61. doi: 10.22124/jart.2021.20476.1310
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