1. Comparing the Zagreb indices of the NEPS of graphsDragan Stevanović, 2012, original scientific article Found in: ključnih besedah Summary of found: ...Zagreb index, Hansen-Vukičević conjecture, NEPS of graphs, Cartesian product of graphs, direct product of graphs,... Keywords: #The #first Zagreb index, #The #second Zagreb index, Hansen-Vukičević conjecture, NEPS of graphs, Cartesian product of graphs, direct product of graphs Published: 15.10.2013; Views: 2428; Downloads: 92 Full text (0,00 KB) |
2. Nove karakterizacije v strukturni teoriji grafovTatiana Romina Hartinger, 2017, doctoral dissertation Found in: ključnih besedah Summary of found: ...graph, K4-minor-free graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong product,... 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: 1738; Downloads: 29 Full text (0,00 KB) |
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4. On normality of n-Cayley graphsKlavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2018, original scientific article Found in: ključnih besedah Summary of found: ...semiregular group, n-Cayley graph, normal n-Cayley graph, Cartesian product... 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 Full text (0,00 KB) |
5. Vertex-transitive graphs and their arc-typesMarston 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: ...we show that the arc-type of a Cartesian product of two "relatively prime" graphs is... Keywords: symmetry type, vertex-transitive graph, arc-transitive graph, Cayley graph, cartesian product, covering graph Published: 03.01.2022; Views: 273; Downloads: 14 Full text (475,17 KB) |