6 papers · 1 filter
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…
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…