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1.
A note on acyclic number of planar graphs
Mirko Petruševski, Riste Škrekovski, 2017, original scientific article

Abstract: The acyclic number ▫$a(G)$▫ of a graph ▫$G$▫ is the maximum order of an induced forest in ▫$G$▫. The purpose of this short paper is to propose a conjecture that ▫$a(G)\geq \left( 1-\frac{3}{2g}\right)n$▫ holds for every planar graph ▫$G$▫ of girth ▫$g$▫ and order ▫$n$▫, which captures three known conjectures on the topic. In support of this conjecture, we prove a weaker result that ▫$a(G)\geq \left( 1-\frac{3}{g} \right)n$▫ holds. In addition, we give a construction showing that the constant ▫$\frac{3}{2}$▫ from the conjecture cannot be decreased.
Keywords: induced forest, acyclic number, planar graph, girth
Published in RUP: 03.01.2022; Views: 895; Downloads: 16
.pdf Full text (227,50 KB)

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: 721; Downloads: 17
.pdf Full text (626,25 KB)

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Vložitev ne-ravninskih grafov : hramba in predstavitev
Đorđe Klisura, 2020, undergraduate thesis

Keywords: planar graph, graph representation, crossing number, graph database
Published in RUP: 02.10.2020; Views: 1092; Downloads: 12
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