几种Cayley图上的验证码与定位码

Identifying and Locating Codes on Some Cayley Graphs

2019年,Junnila,Laihonen和Paris研究了循环图C_(n)(1,d),C_(n)(1,d−1,d)和C_(n)(1,d−1,d,d+1)上的定位码和验证码.本文研究p^(2)阶和2n阶交换群上的八度以内的Cayley图的定位码和验证码,确定它们的最优界,并给出达到最优界的码的例子.这推广了多个关于定位码和验证码的结果.

In 2019,Junnila,Laihonen and Paris studied the identifying codes and locating codes on the circulant graphs C_(n)(1,d),C_(n)(1,d−1,d)and C_(n)(1,d−1,d,d+1).In this paper we study the identifying codes and locating codes of Cayley graphs on the Abelian groups of order p^(2)and order 2n within 8 degrees,determine their optimal bounds,and give some examples that reach the optimal bounds.Our results generalize multiple results on identifying and locating codes.