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Orthogonal graphs modulo power of 2

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arxiv 1901.00998 v1 pith:4KZZJLUH submitted 2019-01-04 math.CO math.RA

classification math.COmath.RA
keywords graphdeltaorthogonalregularworkautomorphismschromaticclasses
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abstract

In this work, we define an orthogonal graph on the set of equivalence classes of $(2\nu + \delta)-$tuples over $\mathbb{Z}_{2^n}$ where $n$ and $\nu$ are positive integers and $\delta = 0, 1$ or $2$. We classify our graph if it is strongly regular or quasi-strongly regular and compute all parameters precisely. We show that our graph is arc transitive. The automorphisms group is given and the chromatic number of the graph except when $\delta = 0$ and $\nu$ is odd is determined. Moreover, we work on subconstituents of this orthogonal graph.

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