On the Q‐Polynomial Property of Bipartite Graphs Admitting a Uniform Structure
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| Format: | Artículo Open Access |
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2025
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| author | Blas Fernández Roghayeh Maleki Štefko Miklavič Giusy Monzillo |
| author_facet | Blas Fernández Roghayeh Maleki Štefko Miklavič Giusy Monzillo Blas Fernández Roghayeh Maleki Štefko Miklavič Giusy Monzillo |
| collection | Wiley Open Access |
| contents | On the Q‐Polynomial Property of Bipartite Graphs Admitting a Uniform Structure Blas Fernández Roghayeh Maleki Štefko Miklavič Giusy Monzillo Journal of Combinatorial Designs 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. 10.1002/jcd.22011 http://creativecommons.org/licenses/by/4.0/ |
| doi_str_mv | 10.1002/jcd.22011 |
| format | Artículo Open Access |
| id | wiley_oa_10_1002_jcd_22011 |
| institution | Wiley Open Access |
| license_str_mv | http://creativecommons.org/licenses/by/4.0/ |
| publishDate | 2025 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | On the Q‐Polynomial Property of Bipartite Graphs Admitting a Uniform Structure Blas Fernández Roghayeh Maleki Štefko Miklavič Giusy Monzillo Journal of Combinatorial Designs On the Q‐Polynomial Property of Bipartite Graphs Admitting a Uniform Structure Blas Fernández Roghayeh Maleki Štefko Miklavič Giusy Monzillo Journal of Combinatorial Designs 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. 10.1002/jcd.22011 http://creativecommons.org/licenses/by/4.0/ |
| title | On the Q‐Polynomial Property of Bipartite Graphs Admitting a Uniform Structure |
| topic | Journal of Combinatorial Designs |
| url | https://onlinelibrary.wiley.com/doi/10.1002/jcd.22011 |