1. Cyclic m-DCI-groups and m-CI-groupsIstván Kovács, Luka Šinkovec, 2025, izvirni znanstveni članek Opis: Based on the earlier work of Li from 1997 and Dobson from 2008, in this paper we complete the classification of cyclic m-DCI-groups and m-CI-groups. For a positive integer m such that m ≥ 3, we show that the group ℤ_(n) is an m-DCI-group if and only if n is not divisible by 8 nor by p² for any odd prime p < m. Furthermore, if m ≥ 6, then we show that ℤn is an m-CI-group if and only if either n ∈ {8, 9, 18}, or n ∉ {8, 9, 18} and n is not divisible by 8 nor by p² for any odd prime p < (m - 1)/2. Ključne besede: Cayley graph, cyclic group, m-CI-group, m-DCI-group Objavljeno v RUP: 01.04.2025; Ogledov: 97; Prenosov: 5
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2. Partial geometries with regular automorphism groups : master’s thesisAdisa Hodžić, 2024, magistrsko delo Ključne besede: (near-) linear space, projective plane, affine plane, partial geometry, generalized quadrangle, strongly regular graph, partial difference set, automorphism group Objavljeno v RUP: 25.12.2024; Ogledov: 946; Prenosov: 4
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4. The core of a vertex-transitive complementary prismMarko Orel, 2023, izvirni znanstveni članek Opis: The complementary prism Γ¯Γ is obtained from the union of a graph Γ and its complement ¯Γ where each pair of identical vertices in Γ and ¯Γ 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 Γ¯Γ is a core, i.e. all its endomorphisms are automorphisms, whenever Γ is a core or its core is a complete graph. Ključne besede: graph homomorphism, complementary prism, self-complementary graph, vertex-transitive graph, core Objavljeno v RUP: 06.11.2023; Ogledov: 1428; Prenosov: 6
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6. The Sierpiński product of graphsJurij Kovič, Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik, 2023, izvirni znanstveni članek Opis: In this paper we introduce a product-like operation that generalizes the construction of the generalized Sierpiński graphs. Let G,H be graphs and let f:V(G)→V(H) be a function. Then the Sierpiński product of graphs G and H with respect to f, denoted by G⊗fH, is defined as the graph on the vertex set V(G)×V(H), consisting of |V(G)| copies of H; for every edge {g,g′} of G▫$ there is an edge between copies ▫$gH and g'H of form \{(g, f(g'), (g', f(g))\}. Some basic properties of the Sierpiński product are presented. In particular, we show that the graph G\otimes_f H is connected if and only if both graphs G and H are connected and we present some conditions that G, \, H must fulfill for G\otimes_f H to be planar. As for symmetry properties, we show which automorphisms of G and H extend to automorphisms of G\otimes_f H. In several cases we can also describe the whole automorphism group of the graph G\otimes_f H. Finally, we show how to extend the Sierpiński product to multiple factors in a natural way. By applying this operation n times to the same graph we obtain an alternative approach to the well-known n-th generalized Sierpiński graph. Ključne besede: Sierpiński graphs, graph products, connectivity, planarity, symmetry Objavljeno v RUP: 06.11.2023; Ogledov: 999; Prenosov: 4
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7. Exploring the bounds and relationships of chemical graph indices : master's thesisArbër Avdullahu, 2023, magistrsko delo Ključne besede: energy of a graph, Randić index, first Zagreb index, IRB index, extremal graph, spectrum, eigenvalue, metaheuristic Objavljeno v RUP: 05.10.2023; Ogledov: 1039; Prenosov: 7
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8. Posplošitev Lijeve domneve in popolna klasifikacija cikličnih m-(D)CI-grup : magistrsko deloLuka Šinkovec, 2023, magistrsko delo Ključne besede: (un)directed Cayley graph, cyclic group, (un)directed circulant graph, Cayley isomorphism, (un)directed CI-graph, (D)CI-group, m-(D)CI-group, key, generalised multiplier Objavljeno v RUP: 11.09.2023; Ogledov: 1173; Prenosov: 19
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