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Hierarchical product graphs and their prime factorization
Wilfried Imrich, Rafał Kalinowski, Monika Pilśniak, 2025, izvirni znanstveni članek

Ključne besede: hierarchical products of graphs, prime factorizations, trees, algorithms
Objavljeno v RUP: 03.11.2025; Ogledov: 257; Prenosov: 1
Celotno besedilo (485,19 KB)

Monoid algebras and graph products
Wilfried Imrich, Igor Klep, Daniel Smertnig, 2025, izvirni znanstveni članek

Opis: In this note, we extend results about unique n^th roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified lexicographic product. We show that these results also hold for graphs with countably many finite connected components, as long as every connected component appears only finitely often (up to isomorphism). The proofs are via monoid algebras and generalized power series rings.
Ključne besede: graph products, monoid algebras, power series rings, uniqueness of roots, cancellation property
Objavljeno v RUP: 21.10.2025; Ogledov: 309; Prenosov: 3
Celotno besedilo (441,50 KB)

On cubic vertex-transitive graphs of given girth
Edward Tauscher Dobson, Ademir Hujdurović, Wilfried Imrich, Ronald Ortner, 2025, izvirni znanstveni članek

Opis: A set of vertices of a graph is distinguishing if the only automorphism that preserves it is the identity. The minimal size of such sets, if they exist, is the distinguishing cost. The distinguishing costs of vertex transitive cubic graphs are well known if they are 1-arc-transitive, or if they have two edge orbits and either have girth 3 or vertex-stabilizers of order 1 or 2. There are many results about vertex-transitive cubic graphs of girth 4 with two edge orbits, but for larger girth almost nothing is known about the distinguishing costs of such graphs. We prove that cubic vertex-transitive graphs of girth 5 with two edge orbits have distinguishing cost 2, and prove the non-existence of infinite 3-arc-transitive cubic graphs of girth 6.
Ključne besede: distinguishing number, distinguishing cost, vertex-transitive cubic graphs, automorphisms
Objavljeno v RUP: 27.08.2025; Ogledov: 747; Prenosov: 4
Celotno besedilo (451,52 KB)
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