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1.
Cubic vertex-transitive graphs admitting automorphisms of large order
Primož Potočnik, Micael Toledo, 2023, izvirni znanstveni članek

Povzetek: A connected graph of order $n$ admitting a semiregular automorphism of order $n/k$ is called a $k$-multicirculant. Highly symmetric multicirculants of small valency have been extensively studied, and several classification results exist for cubic vertex- and arc-transitive multicirculants. In this paper, we study the broader class of cubic vertex-transitive graphs of order $n$ admitting an automorphism of order $n/3$ or larger that may not be semiregular. In particular, we show that any such graph is either a $k$-multicirculant for some $k \le 3$, or it belongs to an infinite family of graphs of girth $6$.
Ključne besede: cubic vertex-transitive graphs, multicirculants, automorphisms of large order
Objavljeno v DiRROS: 18.03.2024; Ogledov: 51; Prenosov: 30
.pdf Celotno besedilo (929,04 KB)
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2.
On orders of automorphisms of vertex-transitive graphs
Primož Potočnik, Micael Toledo, Gabriel Verret, 2024, izvirni znanstveni članek

Povzetek: In this paper we investigate orders, longest cycles and the number of cycles of automorphisms of finite vertex-transitive graphs. In particular, we show that the order of every automorphism of a connected vertex-transitive graph with $n$ vertices and of valence $d$, $d\le 4$, is at most $c_d n$ where $c_3=1$ and $c_4 = 9$. Whether such a constant $c_d$ exists for valencies larger than $4$ remains an unanswered question. Further, we prove that every automorphism $g$ of a finite connected $3$-valent vertex-transitive graph $\Gamma$, $\Gamma \not\cong K_{3,3}$, has a regular orbit, that is, an orbit of $\langle g \rangle$ of length equal to the order of $g$. Moreover, we prove that in this case either $\Gamma$ belongs to a well understood family of exceptional graphs or at least $5/12$ of the vertices of $\Gamma$ belong to a regular orbit of $g$. Finally, we give an upper bound on the number of orbits of a cyclic group of automorphisms $C$ of a connected $3$-valent vertex-transitive graph $\Gamma$ in terms of the number of vertices of $\Gamma$ and the length of a longest orbit of $C$.
Ključne besede: graphs, automorphism groups, vertex-transitive, regular orbit, cubic, tetravalent
Objavljeno v DiRROS: 19.02.2024; Ogledov: 124; Prenosov: 39
.pdf Celotno besedilo (573,20 KB)
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3.
A comparison of models for forecasting the residential natural gas demand of an urban area
Rok Hribar, Primož Potočnik, Jurij Šilc, Gregor Papa, 2019, izvirni znanstveni članek

Povzetek: Forecasting the residential natural gas demand for large groups of buildings is extremely important for efficient logistics in the energy sector. In this paper different forecast models for residential natural gas demand of an urban area were implemented and compared. The models forecast gas demand with hourly resolution up to 60 h into the future. The model forecasts are based on past temperatures, forecasted temperatures and time variables, which include markers for holidays and other occasional events. The models were trained and tested on gas-consumption data gathered in the city of Ljubljana, Slovenia. Machine-learning models were considered, such as linear regression, kernel machine and artificial neural network. Additionally, empirical models were developed based on data analysis. Two most accurate models were found to be recurrent neural network and linear regression model. In realistic setting such trained models can be used in conjunction with a weather-forecasting service to generate forecasts for future gas demand.
Ključne besede: demand forecasting, buildings, energy modeling, forecast accuracy, machine learning
Objavljeno v DiRROS: 15.03.2019; Ogledov: 2237; Prenosov: 1060
.pdf Celotno besedilo (968,06 KB)

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