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1.
The core of a vertex-transitive complementary prism
Marko Orel, 2023, original scientific article

Abstract: The complementary prism ▫$\Gamma \overline{\Gamma}$▫ is obtained from the union of a graph ▫$\Gamma$▫ and its complement ▫$\overline{\Gamma}$▫ where each pair of identical vertices in ▫$\Gamma$▫ and ▫$\overline{\Gamma}$▫ is joined by an edge. It generalizes the Petersen graph, which is the complementary prism of the pentagon. The core of a vertex-transitive complementary prism is studied. In particular, it is shown that a vertex-transitive complementary prism ▫$\Gamma \overline{\Gamma}$▫ is a core, i.e. all its endomorphisms are automorphisms, whenever ▫$\Gamma$▫ is a core or its core is a complete graph.
Keywords: graph homomorphism, complementary prism, self-complementary graph, vertex-transitive graph, core
Published in RUP: 06.11.2023; Views: 772; Downloads: 5
.pdf Full text (305,54 KB)

2.
On 12-regular nut graphs
Nino Bašić, Martin Knor, Riste Škrekovski, 2021, original scientific article

Keywords: nut graph, adjacency matrix, singular matrix, core graph, Fowler construction, regular graph
Published in RUP: 16.07.2021; Views: 1090; Downloads: 25
URL Link to full text

3.
Existence of regular nut graphs for degree at most 11
Patrick W. Fowler, John Baptist Gauci, Jan Goedgebeur, Tomaž Pisanski, Irene Sciriha, 2020, original scientific article

Keywords: nut graph, core graph, regular graph, nullity
Published in RUP: 06.05.2021; Views: 836; Downloads: 0

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