1. Edge regular graph productsBoštjan Frelih, Štefko Miklavič, 2013, original scientific article Found in: ključnih besedah Summary of found: ...edge regular graph, strong product, lexicographic product, deleted lexicographic product, conormal product,... Keywords: edge regular graph, strong product, lexicographic product, deleted lexicographic product, conormal product Published: 15.10.2013; Views: 2340; Downloads: 77 Full text (0,00 KB) 
2. On the split structure of lifted groupsRok Požar, Aleksander Malnič, 2016, original scientific article Abstract: Let ▫$\wp \colon \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations ▫$\rm{CT}_\wp$▫ being abelian. Assuming that a group of automorphisms ▫$G \le \rm{Aut} X$▫ lifts along $\wp$ to a group ▫$\tilde{G} \le \rm{Aut} \tilde{X}$▫, the problem whether the corresponding exact sequence ▫$\rm{id} \to \rm{CT}_\wp \to \tilde{G} \to G \to \rm{id}$▫ splits is analyzed in detail in terms of a Cayley voltage assignment that reconstructs the projection up to equivalence. In the above combinatorial setting the extension is given only implicitly: neither ▫$\tilde{G}$▫ nor the action ▫$G\to \rm{Aut} \rm{CT}_\wp$▫ nor a 2cocycle ▫$G \times G \to \rm{CT}_\wp$▫, are given. Explicitly constructing the cover ▫$\tilde{X}$▫ together with ▫$\rm{CT}_\wp$▫ and ▫$\tilde{G}$▫ as permutation groups on ▫$\tilde{X}$▫ is time and space consuming whenever ▫$\rm{CT}_\wp$▫ is large; thus, using the implemented algorithms (for instance, HasComplement in Magma) is far from optimal. Instead, we show that the minimal required information about the action and the 2cocycle can be effectively decoded directly from voltages (without explicitly constructing the cover and the lifted group); one could then use the standard method by reducing the problem to solving a linear system of equations over the integers. However, along these lines we here take a slightly different approach which even does not require any knowledge of cohomology. Time and space complexity are formally analyzed whenever ▫$\rm{CT}_\wp$▫ is elementary abelian. Found in: ključnih besedah Summary of found: ...algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear... Keywords: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product Published: 15.10.2015; Views: 2102; Downloads: 147 Full text (422,56 KB) This document has more files! More...

3. Nove karakterizacije v strukturni teoriji grafovTatiana Romina Hartinger, 2017, doctoral dissertation Found in: ključnih besedah Summary of found: ...1perfectly orientable graph, structural characterization of families of graphs, chordal... ...cobipartite graph, K4minorfree graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong... Keywords: 1perfectly orientable graph, structural characterization of families of graphs, chordal graph, interval graph, circular arc graph, cograph, blockcactus graph, cobipartite graph, K4minorfree graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong product, price of connectivity, cycle transversal, path transversal Published: 09.11.2017; Views: 1739; Downloads: 29 Full text (0,00 KB) 
4. Characterizations of minimal dominating sets and the welldominated property in lexicographic product graphsAdemir Hujdurović, Didem Gozüpek, Martin Milanič, 2017, original scientific article Found in: ključnih besedah Summary of found: ...množica, dobro dominiran graf, nesvodljiva dominantna množica, lexico graphic product of graphs, minimal dominating set,, welldominated... Keywords: lekisikografski product grafov, minimalna dominantna množica, dobro dominiran graf, nesvodljiva dominantna množica, lexicographic product of graphs, minimal dominating set, welldominated graph, irreducible dominating set Published: 14.11.2017; Views: 1543; Downloads: 60 Full text (0,00 KB) 
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6. On normality of nCayley graphsKlavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2018, original scientific article Found in: ključnih besedah Summary of found: ...vertextransitive grapht, Cayley graph, semiregular group, nCayley graph, normal... Keywords: vertextransitive grapht, Cayley graph, semiregular group, nCayley graph, normal nCayley graph, Cartesian product Published: 05.04.2018; Views: 1970; Downloads: 127 Full text (0,00 KB) 
7. Vertextransitive graphs and their arctypesMarston D. E. Conder, Tomaž Pisanski, Arjana Žitnik, 2017, original scientific article Abstract: Let ▫$X$▫ be a finite vertextransitive graph of valency ▫$d$▫, and let ▫$A$▫ be the full automorphism group of ▫$X$▫. Then the arctype 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 selfpaired 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 arcreversal. The arctype 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 selfpaired orbits, and ▫$m_1,m_1, m_2,m_2, \dots, m_s,m_s$▫ are the sizes of the nonselfpaired orbits, in descending order. In this paper, we find the arctypes of several families of graphs. Also we show that the arctype of a Cartesian product of two "relatively prime" graphs is the natural sum of their arctypes. 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 vertextransitive graph with the given partition as its arctype. Found in: ključnih besedah Summary of found: ...Let ▫$X$▫ be a finite vertextransitive graph of valency ▫$d$▫, and let ▫$A$▫ be... ...show that the arctype of a Cartesian product of two "relatively prime" graphs is the... Keywords: symmetry type, vertextransitive graph, arctransitive graph, Cayley graph, cartesian product, covering graph Published: 03.01.2022; Views: 273; Downloads: 14 Full text (475,17 KB) 