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1.
Edge regular graph products
Boštjan Frelih, Štefko Miklavič, 2013, original scientific article

Found in: ključnih besedah
Summary of found: ...edge regular graph, strong product, lexicographic product, deleted lexicographic product, co-normal product,...
Keywords: edge regular graph, strong product, lexicographic product, deleted lexicographic product, co-normal product
Published: 15.10.2013; Views: 2340; Downloads: 77
URL Full text (0,00 KB)

2.
On the split structure of lifted groups
Rok 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 2-cocycle ▫$G \times G \to \rm{CT}_\wp$▫, 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 2-cocycle 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
.pdf Full text (422,56 KB)
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3.
Nove karakterizacije v strukturni teoriji grafov
Tatiana Romina Hartinger, 2017, doctoral dissertation

Found in: ključnih besedah
Summary of found: ...1-perfectly orientable graph, structural characterization of families of graphs, chordal... ...cobipartite graph, K4-minor-free graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong...
Keywords: 1-perfectly orientable graph, structural characterization of families of graphs, chordal graph, interval graph, circular arc graph, cograph, block-cactus graph, cobipartite graph, K4-minor-free 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
URL Full text (0,00 KB)

4.
Characterizations of minimal dominating sets and the well-dominated property in lexicographic product graphs
Ademir 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,, well-dominated...
Keywords: lekisikografski product grafov, minimalna dominantna množica, dobro dominiran graf, nesvodljiva dominantna množica, lexicographic product of graphs, minimal dominating set, well-dominated graph, irreducible dominating set
Published: 14.11.2017; Views: 1543; Downloads: 60
URL Full text (0,00 KB)

5.
On 2-distance-balanced graphs
Štefko Miklavič, Boštjan Frelih, 2018, original scientific article

Found in: ključnih besedah
Summary of found: ...n-distance-balanced graph, cartesian product, lexicographic product...
Keywords: n-distance-balanced graph, cartesian product, lexicographic product
Published: 07.02.2018; Views: 2422; Downloads: 115
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6.
On normality of n-Cayley graphs
Klavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2018, original scientific article

Found in: ključnih besedah
Summary of found: ...vertex-transitive grapht, Cayley graph, semiregular group, n-Cayley graph, normal...
Keywords: vertex-transitive grapht, Cayley graph, semiregular group, n-Cayley graph, normal n-Cayley graph, Cartesian product
Published: 05.04.2018; Views: 1970; Downloads: 127
URL Full text (0,00 KB)

7.
Vertex-transitive graphs and their arc-types
Marston D. E. Conder, Tomaž Pisanski, Arjana Žitnik, 2017, original scientific article

Abstract: 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.
Found in: ključnih besedah
Summary of found: ...Let ▫$X$▫ be a finite vertex-transitive graph of valency ▫$d$▫, and let ▫$A$▫ be... ...show that the arc-type of a Cartesian product of two "relatively prime" graphs is the...
Keywords: symmetry type, vertex-transitive graph, arc-transitive graph, Cayley graph, cartesian product, covering graph
Published: 03.01.2022; Views: 273; Downloads: 14
.pdf Full text (475,17 KB)

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