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Octavio B. Zapata-Fonseca

Publications and source records attributed to Octavio B. Zapata-Fonseca.

3 recordsLinked to original sources
arXiv2026

Logical aspects of isomorphism of controllable graphs and cospectrality of distance-regularized graphs

We consider isomorphism of controllable graphs and cospectrality of distance-regularized graphs (which are known to be distance-regular or distance-biregular) in relation to logical definability. While most characterizations of these equivalence relations for such graph classes are of algebraic and spectral flavor, here we inject tools from first-order logic, extending and unifying several existing results.

math.CO↗
arXiv2025

Quasi-strongly regular graphs on the flags of symmetric designs

This paper was inspired by a paper by Blokhuis and Brouwer [Designs, Codes and Cryptography 65, 2012] in which a definition of a graph on the flags of a biplane is given, and they prove that the graph corresponding to the unique $(11,5,2)$-biplane is determined by its spectrum. It is also inspired by the different definition of flag-graph seen in the context of maps and abstract polytopes. Here we use this definition for $(v,k,λ)$-BIBDs, and prove that if the design is symmetric then the graph is quasi-strongly regular. We will also use the definition given by Blokhuis and Brouwer for the case of biplanes and prove that this too, is a QSRG, (with different parameters). We investigate whether these graphs are determined by their spectra for some of the known biplanes.

math.CO↗