### Cycle Discrepancy of Cubic Toeplitz Graphs

#### Abstract

*A Toeplitz graph is one whose adjacency matrix is a Toeplitz matrix. A Toeplitz matrix is also known as a constant diagonal matrix. This paper defines cubic Toeplitz graphs and establishes that the cycle discrepancy of a cubic Toeplitz graph is at most 1. That is*cycdisc(G) ≤ 1

*, where G is a cubic Toeplitz graph. Further this bound is shown to be tight.*

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