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1.
Classification of cubic vertex-transitive tricirculants
Primož Potočnik, Micael Toledo, 2020, original scientific article

Keywords: graph, cubic, semiregular automorphism, tricirculant, vertex-transitive
Published in RUP: 03.01.2022; Views: 795; Downloads: 40
.pdf Full text (1,18 MB)

2.
Mathematical aspects of fullerenes
Vesna Andova, František Kardoš, Riste Škrekovski, 2016, original scientific article

Abstract: Fullerene graphs are cubic, 3-connected, planar graphs with exactly 12 pentagonal faces, while all other faces are hexagons. Fullerene graphs are mathematical models of fullerene molecules, i.e., molecules comprised only by carbon atoms different than graphites and diamonds. We give a survey on fullerene graphs from our perspective, which could be also considered as an introduction to this topic. Different types of fullerene graphs are considered, their symmetries, and construction methods. We give an overview of some graph invariants that can possibly correlate with the fullerene molecule stability, such as: the bipartite edge frustration, the independence number, the saturation number, the number of perfect matchings, etc.
Keywords: fullerene, cubic graph, planar graph, topological indices
Published in RUP: 03.01.2022; Views: 703; Downloads: 17
.pdf Full text (626,25 KB)

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Detecting strong cliques
Ademir Hujdurović, Martin Milanič, Bernard Ries, 2019, original scientific article

Keywords: strong clique, weakly chordal graph, line graph, cubic graph
Published in RUP: 30.06.2019; Views: 2141; Downloads: 207
URL Link to full text

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Odd extensions of transitive groups via symmetric graphs - The cubic case
Klavdija Kutnar, Dragan Marušič, 2018, original scientific article

Abstract: When dealing with symmetry properties of mathematical objects, one of the fundamental questions is to determine their full automorphism group. In this paper this question is considered in the context of even/odd permutations dichotomy. More precisely: when is it that the existence of automorphisms acting as even permutations on the vertex set of a graph, called even automorphisms, forces the existence of automorphisms that act as odd permutations, called odd automorphisms. As a first step towards resolving the above question, complete information on the existence of odd automorphisms in cubic symmetric graphs is given.
Keywords: automorphism group, arc-transitive, even permutation, odd permutation, cubic symmetric graph
Published in RUP: 19.11.2018; Views: 1975; Downloads: 198
URL Link to full text

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