14 citations · 27 across the 9 of their papers we have counts for
11 papers
Theoretical and Computational Approaches to Determining Sets of Orders for -Graphs
L. C. Eze, R. Jajcay, T. Jajcayová +1
The Cage Problem requires for a given pair of integers the determination of the order of a smallest -regular graph of girth . We address a more general v…
On -Graphs without -Cycles
Leonard Chidiebere Eze, Robert Jajcay, Jorik Jooken
A -graph is a -regular graph of girth which does not contain cycles of length . Such graphs are known to exist for all parameter pairs $k \geq 3,…
Analogues of Bermond-Bollobás Conjecture for Cages Yield Expander Families
Leonard Chidiebere Eze, Robert Jajcay
This paper presents a possible link between Cages and Expander Graphs by introducing three interconnected variants of the Bermond and Bollobás Conjecture, originally formulated in…
On vertex-girth-regular graphs: (Non-)existence, bounds and enumeration
Robert Jajcay, Jorik Jooken, István Porupsánszki
A vertex-girth-regular -graph is a -regular graph of girth and order in which every vertex belongs to exactly cycles of length . While all vertex-tr…
Cyclic complementary extensions and skew-morphisms
Kan Hu, Robert Jajcay
A cyclic complementary extension of a finite group is a finite group which contains and a cyclic subgroup such that and . For any fixed gene…
Bipartite Biregular Cages and Block Designs
Gabriela Araujo-Pardo, Alejandra Ramos-Rivera, Robert Jajcay
A bipartite biregular -graph is a bipartite graph of even girth having the degree set and satisfying the additional property that the vertices in the sam…
Inverse monoids of partial graph automorphisms
Robert Jajcay, Tatiana Jajcayova, Nóra Szakács +1
A partial automorphism of a finite graph is an isomorphism between its vertex induced subgraphs. The set of all partial automorphisms of a given finite graph forms an inverse monoi…
On a problem of Bermond and Bollobás
Slobodan Filipovski, Robert Jajcay
Let be the order of the largest undirected graphs of maximum degree and diameter , and let be the corresponding Moore bound. In this paper, we give a posi…
On certain edge-transitive bicirculants
Robert Jajcay, Štefko Miklavič, Primož Šparl +1
A graph of even order is a bicirculant if it admits an automorphism with two orbits of equal length. Symmetry properties of bicirculants, for which at least one of the induced…
Symmetry properties of generalized graph truncations
Eduard Eiben, Robert Jajcay, Primož Šparl
In the generalized truncation construction, one replaces each vertex of a -regular graph with a copy of a graph of order . We investigate the symmetry properties of t…
Cayley properties of merged Johnson graphs
Gareth A. Jones, Robert Jajcay
Extending earlier results of Godsil and of Dobson and Malnic on Johnson graphs, we characterise those merged Johnson graphs which are Cayley graphs, that is, which are…