Identifying Codes of Degree 4 Cayley Graphs over Abelian Groups

TL;DR

This paper introduces a broad family of identifying codes for degree 4 Cayley graphs over finite Abelian groups, including well-known graphs like tori and Kronecker products, with applications in adaptive identification.

Contribution

It presents a new construction of identifying codes for a wide class of Cayley graphs, some of which are also perfect, expanding their applicability.

Findings

Codes are applicable to well-known graphs like tori and twisted tori.

Some codes constructed are also perfect.

Application example for adaptive identification provided.

Abstract

In this paper a wide family of identifying codes over regular Cayley graphs of degree four which are built over finite Abelian groups is presented. Some of the codes in this construction are also perfect. The graphs considered include some well-known graphs such as tori, twisted tori and Kronecker products of two cycles. Therefore, the codes can be used for identification in these graphs. Finally, an example of how these codes can be applied for adaptive identification over these graphs is presented.