给定直径的二部图中生成树的最大数目
Maximum number of spanning trees in bipartite graphs with a given diameter
- Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
- MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles（航空飞行器数学建模与高性能计算工信部重点实验室）
- University of Niš（尼什大学）
- University of Primorska（沿海大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文确定了给定阶数和直径的二部图中生成树数量最多的所有图，为可靠二部网络设计提供极值刻画与结构参考。
中文摘要 AI 辅助
生成树的数量是一个经典的图不变量，也是网络可靠性的重要度量，因为它计算了能够维持网络中通信的最小连通生成子结构的数量。设 $\mathcal{B}(n,d)$ 为阶数为 $n$、直径为 $d$ 的连通二部图的集合。受具有固定阶数和直径的二部网络模型的可靠性设计问题的启发，本文确定了 $\mathcal{B}(n,d)$ 中具有最大生成树数量的所有图。该结果给出了在给定阶数和直径约束下具有最多连通生成骨干的二部网络拓扑的极值刻画，并为可靠二部网络的设计提供了结构参考。
英文摘要
The number of spanning trees is a classical graph invariant and an important measure of network reliability, as it counts the minimal connected spanning substructures that can maintain communication in a network. Let $\mathcal{B}(n,d)$ be the set of connected bipartite graphs of order $n$ and diameter $d$. Motivated by reliability design problems for bipartite network models with fixed order and diameter, this paper determines all graphs with the maximum number of spanning trees in $\mathcal{B}(n,d)$. The result gives an extremal characterization of bipartite network topologies with the largest number of connected spanning backbones under prescribed order and diameter constraints, and provides a structural reference for the design of reliable bipartite networks.
