AI 中文总结
研究高围长的强正则带号图，证明围长为4的二分图由加权矩阵设计和对称块设计分类，围长为5的易于描述，围长更高的不存在，围长为4的非二分图未解决。
AI 中文摘要
强正则带号图是强正则图在带号图领域的扩展，即每条边为正或负的图。与普通强正则图不同，大多数围长为4或更高的带号对应物可用已知结构描述。我们证明，围长为4的二分图由两种设计分类：加权矩阵设计和对称块设计。围长为5的很少且易于描述。围长更高的不存在。围长为4的非二分图尚未解决。
英文摘要
Strongly regular signed graphs are an extension of strongly regular graphs to the realm of signed graphs, that is, graphs where each edge is positive or negative. Unlike with ordinary strongly regular graphs, most kinds of signed counterparts with girth 4 or higher are describable in terms of known structures. We prove that those with girth 4 that are bipartite are classified by designs of two kinds: weighing matrix designs and symmetric block designs. Those of girth 5 are few and readily described. There are none of higher girth. Those with girth 4 that are not bipartite are unsolved.
Comments6 pp
