Identifying Codes in the Complementary Prism of Cycles

TL;DR

This paper determines the minimum size of identifying codes in the complementary prism of cycles and explores the clique-width properties of such graph constructions, with implications for algorithms.

Contribution

It provides a precise asymptotic value for the minimum identifying code size in the complementary prism of cycles and analyzes the clique-width of these graphs.

Findings

Minimum identifying code size is approximately 7n/9 for cycles of order n.

Clique-width of the complementary prism is at most four times that of the original graph.

Discusses algorithmic implications of clique-width bounds.

Abstract

We show that an identifying code of minimum order in the complementary prism of a cycle of order $n$ has order $7n/9+\Theta(1)$. Furthermore, we observe that the clique-width of the complementary prism of a graph of clique-width $k$ is at most $4k$, and discuss some algorithmic consequences.