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On the hamiltonicity problem of bicirculants: a reduction to cyclic Haar graphs
Simona Bonvicini, Tomaž Pisanski, Arjana Žitnik
A bicirculant is a regular graph that admits an automorphism having two vertex-orbits of the same size. A bicirculant can be described as follows. Given an integer and se…
The Grünbaum--Rigby configuration as a special Kárteszi configuration
Gábor Gévay, György Kiss, Tomaž Pisanski
In 1990, Branko Grünbaum and John Rigby presented a 4-configuration, known today as the \emph{Grünbaum--Rigby configuration}; it is denoted by . Independently an…
The Möbius-Kantor graph is a faithful unit-distance graph
Nino Bašić, Gábor Gévay, Tomaž Pisanski
In this paper, it has been shown that the generalized Petersen graph , also known as the Möbius-Kantor graph, admits a faithful unit-distance representation in t…
Polycyclic Geometric Realizations of the Gray Configuration
Leah Wrenn Berman, Gábor Gévay, Tomaž Pisanski
The Gray configuration is a (27_3) configuration which typically is realized as the points and lines of the 3 x 3 x 3 integer lattice. It occurs as a member of an infinite family o…
Classification of quartic bicirculant nut graphs
Ivan Damnjanović, Nino Bašić, Tomaž Pisanski +1
A graph is called a nut graph if zero is its eigenvalue of multiplicity one and its corresponding eigenvector has no zero entries. A graph is a bicirculant if it admits an automorp…
On singular signed graphs with nullspace spanned by a full vector: Signed nut graphs
Nino Bašić, Patrick W. Fowler, Tomaž Pisanski +1
A signed graph has edge weights drawn from the set , and is termed sign-balanced if it is equivalent to an unsigned graph under the operation of sign switching; otherwis…