维纳指数与不规则正方形单元配置的平均距离
Wiener and Average Distance of Irregular Square-Cell Configuration
AI总结：
本文研究了不规则边界正方形单元配置的维纳指数和平均距离，推导了通用表达式，揭示了不规则性对距离分布的影响，并为对称和非对称正方形单元图提供统一框架。
摘要：
正方形晶格的子图，其所有内面均为4-循环，称为正方形单元配置。先前工作已为对称正方形单元配置提供了顶点对总距离和平均距离的显式表达式，包括如H(n)、T(n,k)和BT(n,k1,k2)等结构良好的家族。本文进一步将正方形单元配置从规则边界扩展到不规则边界，这些边界不表现出完全的规则性或对称性。我们为这种不规则配置推导了维纳指数和平均距离的通用表达式，结合了组合和结构变化。结果展示了不规则性如何影响距离的增长和分布，并提供了一个包含对称和非对称正方形单元图的统一框架。这种一般化为具有复杂或扰动几何特征的正方形单元框架提供了新的见解。
英文摘要：
A subgraph of the square lattice with all of its inner faces being 4-cycles is called a square-cell configuration. Prior work has provided explicit expressions for the total and average distances between vertex pairs in symmetric square-cell configurations, including well-structured families such as hexagonal square-cell configurations $H(n)$, trapezium square-cell configurations $T(n,k)$, and bitrapezium square-cell configurations $BT(n,k_1,k_2)$. In this article, we further extend the square-cell configuration from regular boundaries to irregular boundaries, which do not exhibit complete regularity or symmetry in their structure. We find the generalized expressions for the Wiener index and average distance of such irregular configurations, incorporating combinatorial and structural variations. Our results demonstrate how irregularity affects the growth and distribution of pairwise distances and provide a unifying framework that includes both symmetric and asymmetric square-cell graphs as exceptional cases. This generalization provides novel insights into the structural behaviour of square-cell frameworks characterized by complex or perturbed geometries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
