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1.
Vertex-transitive graphs and their arc-types
Marston D. E. Conder, Tomaž Pisanski, Arjana Žitnik, 2017, izvirni znanstveni članek

Opis: Let ▫$X$▫ be a finite vertex-transitive graph of valency ▫$d$▫, and let ▫$A$▫ be the full automorphism group of ▫$X$▫. Then the arc-type of ▫$X$▫ is defined in terms of the sizes of the orbits of the stabiliser ▫$A_v$▫ of a given vertex ▫$v$▫ on the set of arcs incident with ▫$v$▫. Such an orbit is said to be self-paired if it is contained in an orbit ▫$\Delta$▫ of ▫$A$▫ on the set of all arcs of v$X$▫ such that v$\Delta$▫ is closed under arc-reversal. The arc-type of ▫$X$▫ is then the partition of ▫$d$▫ as the sum ▫$n_1 + n_2 + \dots + n_t + (m_1 + m_1) + (m_2 + m_2) + \dots + (m_s + m_s)$▫, where ▫$n_1, n_2, \dots, n_t$▫ are the sizes of the self-paired orbits, and ▫$m_1,m_1, m_2,m_2, \dots, m_s,m_s$▫ are the sizes of the non-self-paired orbits, in descending order. In this paper, we find the arc-types of several families of graphs. Also we show that the arc-type of a Cartesian product of two "relatively prime" graphs is the natural sum of their arc-types. Then using these observations, we show that with the exception of ▫$1+1$▫ and ▫$(1+1)$▫, every partition as defined above is \emph{realisable}, in the sense that there exists at least one vertex-transitive graph with the given partition as its arc-type.
Ključne besede: symmetry type, vertex-transitive graph, arc-transitive graph, Cayley graph, cartesian product, covering graph
Objavljeno v RUP: 03.01.2022; Ogledov: 586; Prenosov: 16
.pdf Celotno besedilo (475,17 KB)

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The relationship between income and tourism demand : old findings and new research
Helena Nemec Rudež, 2018, pregledni znanstveni članek

Ključne besede: income elasticity, tourism demand, luxury product, necessity
Objavljeno v RUP: 21.11.2021; Ogledov: 762; Prenosov: 28
.pdf Celotno besedilo (1,90 MB)

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On 2-distance-balanced graphs
Boštjan Frelih, Štefko Miklavič, 2018, izvirni znanstveni članek

Ključne besede: n-distance-balanced graph, cartesian product, lexicographic product
Objavljeno v RUP: 07.02.2018; Ogledov: 2813; Prenosov: 118
.pdf Celotno besedilo (289,62 KB)

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