In this paper, we formally introduce the concept of a row-sum matrix over an arbitrary group G. When G is cyclic, these types of matrices have been widely used to build uniform 2-factorizations of small Cayley graphs (or, Cayley subgraphs of blown-up cycles), which themselves factorize complete (equipartite) graphs.

Here, we construct row-sum matrices over a class of non-abelian groups, the generalized dihedral groups, and we use them to construct uniform 2-factorizations that solve infinitely many open cases of the Hamilton-Waterloo problem, thus filling up large parts of the gaps in the spectrum of orders for which such factorizations are known to exist.

在本文中，我们正式引入了任意群G上的行和矩阵的概念。当G是循环时，这些类型的矩阵已广泛用于构建小凯莱图（或放大循环的凯莱子图）的统一 2 因式分解，其本身可因式分解完整（等分）图。

在这里，我们在一类非阿贝尔群（广义二面群）上构造行和矩阵，并使用它们构造一致的 2 因式分解来解决汉密尔顿-滑铁卢问题的无限多个开放情况，从而填充大部分已知存在此类因式分解的阶数谱中的间隙。