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A unified framework for existing and new constructions of Neumaier graphs
Aida Abiad, Wouter Castryck, Maarten De Boeck +2
A Neumaier graph is a non-complete edge-regular graph containing a regular clique; it is called strictly Neumaier if it is not strongly regular. In this paper we present a construc…
A linear programming bound for sum-rank metric codes
Aida Abiad, Alexander L. Gavrilyuk, Antonina P. Khramova +1
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances,…
Eigenvalue Bounds for Sum-Rank-Metric Codes
Aida Abiad, Antonina P. Khramova, Alberto Ravagnani
We consider the problem of deriving upper bounds on the parameters of sum-rank-metric codes, with focus on their dimension and block length. The sum-rank metric is a combination of…
A switching method for constructing cospectral gain graphs
Aida Abiad, Francesco Belardo, Antonina P. Khramova
A gain graph over a group , also referred to as -gain graph, is a graph where an element of a group , called gain, is assigned to each oriented edge, in such a way that th…
Constructing cospectral hypergraphs
Aida Abiad, Antonina P. Khramova
Spectral hypergraph theory mainly concerns using hypergraph spectra to obtain structural information about the given hypergraphs. The study of cospectral hypergraphs is important s…
Extending a conjecture of Graham and Lovász on the distance characteristic polynomial
Aida Abiad, Boris Brimkov, Sakander Hayat +2
Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order is unimodal with the maximum val…