What type of study is this?

This is a Quantitative Study study.

October 12, 2025Open Access

On the Q Q‐Polynomial Property of Bipartite Graphs Admitting a Uniform Structure

Puntos clave

Sufficient conditions are established for a uniform structure in bipartite graphs to admit a dual adjacency matrix.
The results indicate that full bipartite graphs of dual polar graphs are polynomial, highlighting their structure.
The dual adjacency matrix candidates are defined relative to the adjacency matrix and eccentricity metrics.
This work builds on prior work in coding and design theories, showing practical implications for graph classifications.

Resumen

ABSTRACT Let denote a finite, connected graph with vertex set . Fix and let denote the eccentricity of . For mutually distinct scalars define a diagonal matrix as follows: for we let , where denotes the shortest path length distance function of . We say that is a dual adjacency matrix candidate of with respect to if the adjacency matrix of and satisfy for some scalars . Assume now that is uniform with respect to in the sense of Terwilliger Coding theory and design theory, Part I, IMA Vol. Math. Appl., 20 , 193–212 (1990). In this paper, we give sufficient conditions on the uniform structure of , such that admits a dual adjacency matrix candidate with respect to . As an application of our results, we show that the full bipartite graphs of dual polar graphs are ‐polynomial.

Leer artículo completoexternamente

Preguntar a la IA

Me gusta

Guardar

Ver artículo completo