Abstract: The undirected double loop networkG(N;±s₁,±s₂) is a Cayley graph with degree 4.The relationship between the four parameters of the L- shape tile and the smallest non-negative solution and the smallest cross solution of the congruence equationxs₁+ys₂≡0modN is obtained.So the new diameter of G(N;±s₁,±s₂)can be represented by the four parameters of the L-shape tile.

Key words: undirected double loop network, L- shape tile, the smallest non-negative solution, the smallest cross solution

摘要： 无向双环网络G(N;±s₁,±s₂)是一种度为4的Cayley图。研究了无向双环网络的L-型瓦的4个参数与xs₁+ys₂≡0modN的最小非负解和最小交叉解的关系，从而通过L-型瓦的4个参数可以得出无向双环网一种新的直径公式。

关键词: 无向双环网, L-型瓦, 最小非负解, 最小交叉解