Andrea Švob

Switching graphs and designs

Aida Abiad, Dean Crnković, Louka Peters +1

Switching methods can be seen as certain local transformations that do not alter their basic parameters of a combinatorial structure. Efforts have been devoted in the literature to…

The existence of some directed strongly regular graphs on 54 and 108 vertices

Dean Crnković, Andrea Švob, Matea Zubović Žutolija

In this paper, we prove the existence of directed strongly regular graphs with parameters (108,11,3,2,1), (108,14,10,0,2), (108,22,12,6,4), (108,23,9,8,4), (108,25,15,8,5), (108,34…

Complex generalised weighing matrices in centraliser algebras of monomial representations

Ronan Egan, Padraig Ó Catháin, Andrea Švob

An $n \times n$ matrix $W$ with exactly $w$ non-zero entries taken from the set of $k^{th}$ complex roots of unity in each row and column satisfying $W W^{*} = w I_{n}$ is a com…

New directed strongly regular graphs on 60 vertices

Dean Crnkovic, Andrea Svob, Matea Zubovic Zutolija

We prove the existence of directed strongly regular graphs with parameters (60,21,11,6,8), (60,22,12,8,8), (60,24,10,9,10), (60,25,17,8,12), (60,27,21,12,12) and (60,28,20,14,12).…

math.CO2025

A universal theory of switching for combinatorial objects, and applications to complex Hadamard matrices

Dean Crnković, Ronan Egan, Andrea Švob

The concept of switching has arisen in several different areas within combinatorics. The act of switching usually transforms a combinatorial object into a non-isomorphic object of…

Constructions of self-orthogonal and LCD subspace codes

Dean Crnković, Keita Ishizuka, Hadi Kharaghani +2

Recently, the notions of self-orthogonal subspace codes and LCD subspace codes were introduced, and LCD subspace codes obtained from mutually unbiased weighing matrices were studie…

Transitive regular $q$ -analogs of graphs

Dean Crnkovic, Vedrana Mikulic Crnkovic, Andrea Svob +1

In 1976, Delsarte introduced the notion of $q$ -analogs of designs, and $q$ -analogs of graphs were introduced recently by M. Braun et al. In this paper, we extend that study by givi…

$q$ -Analogs of divisible design graphs and Deza graphs

Dean Crnkovic, Maarten De Boeck, Francesco Pavese +1

Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. In this paper, we introduce the notion of $q$ -analogs of divisible design graphs and show tha…

A construction of directed strongly regular graphs with parameters (63,11,8,1,2)

Andries E. Brouwer, Dean Crnković, Andrea Švob

In this paper, we prove the existence of directed strongly regular graphs with parameters $(63, 11, 8, 1, 2)$ . We construct a pair of nonisomorphic dsrg(63,11,8,1,2), where one is obta…

math.CO2023

Doubly even self-orthogonal codes from quasi-symmetric designs

Dean Crnković, Doris Dumičić Danilović, Ana Šumberac +1

In this paper, we give a construction of doubly even self-orthogonal codes from quasi-symmetric designs. Further, we study orbit matrices of quasi-symmetric designs and give a cons…

math.CO2023

Neighbour-transitive codes in Kneser graphs

Dean Crnković, Daniel R. Hawtin, Nina Mostarac +1

A code $C$ is a subset of the vertex set of a graph and $C$ is $s$ -neighbour-transitive if its automorphism group $Aut (C)$ acts transitively on each of the first $s + 1$ parts…

math.CO2022

LCD subspace codes

Dean Crnkovic, Andrea Svob

A subspace code is a nonempty set of subspaces of a vector space $F_{q}^{n}$ . Linear codes with complementary duals, or LCD codes, are linear codes whose intersection with thei…

Switching for 2-designs

Dean Crnković, Andrea Švob

In this paper we introduce a switching for 2-designs. We illustrate this method by applying it to some symmetric (64,28,12) designs. In that way we obtain six new symmetric (64,28,…

New constructions of divisible design Cayley graphs

Dean Crnković, Andrea Švob

Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. Further, divisible design graphs which can be obtained as Cayley graphs were recently studied…

New symmetric 2-(176,50,14) designs

Dean Crnković, Andrea Švob

In this paper we construct two new symmetric designs with parameters 2-(176,50,14) as designs invariant under certain subgroups of the full automorphism group of the Higman design.…

Neighbour-Transitive Codes and Partial Spreads in Generalised Quadrangles

Dean Crnković, Daniel R. Hawtin, Andrea Ŝvob

A code $C$ in a generalised quadrangle $Q$ is defined to be a subset of the vertex set of the point-line incidence graph $Γ$ of $Q$ . The minimum dista…

$q$ -Analogs of strongly regular graphs

Michael Braun, Dean Crnković, Maarten De Boeck +2

We introduce the notion of q-analogs of strongly regular graphs and give several examples of such structures. We prove a necessary condition on the parameters, show the connection…