AI 中文总结
针对Conlon和Lee提出的问题，构造了双参数族非半范数2-连通强支配图，通过双根块循环融合实现，确定K_{2,m}的循环融合准则，还分类了相关外平面图强支配图及块。
AI 中文摘要
Conlon和Lee提出了在范数图和偶路径之外寻找强支配图的问题。我们构造了一个双参数族的两两非同构2-连通强支配图，这些图不是半范数图，因此不属于之前针对符号强支配确定的两类例子。该构造使用双根块的循环融合。对于根可逆块，我们通过转移算子的局部偶Schatten不等式刻画了所有偶循环融合的生成。我们确定了K_{2,m}（根位于大小为m的部分）的该准则：当且仅当m为偶数时成立。我们还对连通外平面图强支配图以及满足通用循环准则的连通根可逆外平面块进行了分类。
英文摘要
Conlon and Lee asked for strongly dominating graphs beyond norming graphs and even paths. We construct a two-parameter family of pairwise non-isomorphic $2$-connected strongly dominating graphs that are not seminorming, and hence lie outside the two classes of examples previously identified for signed strong domination. The construction uses cyclic amalgamation of two-rooted blocks. For root-reversible blocks, we characterize the generation of all even cyclic amalgams by local even-Schatten inequalities for transfer operators. We determine this criterion for $K_{2,m}$, with the roots in the part of size $m$: it holds exactly when $m$ is even. We also classify the connected outerplanar strongly dominating graphs and the connected root-reversible outerplanar blocks satisfying the universal cyclic criterion.
