标题： 平衡Cayley图和平衡平面图 显示英文标题

标题： Balanced Cayley graphs and balanced planar graphs

摘要： 一个平衡图是一个没有长度为 2 模 4 的诱导环的二分图。 这些图出现在线性规划中。 我们关注平衡图的图代数性质，以证明对阿贝尔群上的平衡Cayley图的完整分类。 此外，在本文第5节中，我们证明不存在三次平衡平面图。 最后，还提出了关于平衡正则图的一些显著猜想。 显示英文摘要

摘要： A balanced graph is a bipartite graph with no induced circuit of length 2 mod 4. These graphs arise in linear programming. We focus on graph-algebraic properties of balanced graphs to prove a complete classification of balanced Cayley graphs on abelian groups. Moreover, in Section 5 of this paper, we prove that there is no cubic balanced planar graph. Finally, some remarkable conjectures for balanced regular graphs are also presented.