Iskanje po repozitoriju

Ključne besede: (near-) linear space, projective plane, affine plane, partial geometry, generalized quadrangle, strongly regular graph, partial difference set, automorphism group
Objavljeno v RUP: 25.12.2024; Ogledov: 913; Prenosov: 4
Celotno besedilo (1,22 MB)

Opis: The complementary prism ▫$\Gamma \overline{\Gamma}$▫ is obtained from the union of a graph ▫$\Gamma$▫ and its complement ▫$\overline{\Gamma}$▫ where each pair of identical vertices in ▫$\Gamma$▫ and ▫$\overline{\Gamma}$▫ is joined by an edge. It generalizes the Petersen graph, which is the complementary prism of the pentagon. The core of a vertex-transitive complementary prism is studied. In particular, it is shown that a vertex-transitive complementary prism ▫$\Gamma \overline{\Gamma}$▫ is a core, i.e. all its endomorphisms are automorphisms, whenever ▫$\Gamma$▫ is a core or its core is a complete graph.
Ključne besede: graph homomorphism, complementary prism, self-complementary graph, vertex-transitive graph, core
Objavljeno v RUP: 06.11.2023; Ogledov: 1378; Prenosov: 6
Celotno besedilo (305,54 KB)

Opis: In this paper we introduce a product-like operation that generalizes the construction of the generalized Sierpiński graphs. Let ▫$G, \, H$▫ be graphs and let ▫$f: V(G) \to V(H)$▫ be a function. Then the Sierpiński product of graphs ▫$G$▫ and ▫$H$▫ with respect to ▫$f$▫, denoted by ▫$G\otimes_f H$▫, is defined as the graph on the vertex set ▫$V(G) \times V(H)$▫, consisting of ▫$|V(G)|$▫ copies of ▫$H$▫; for every edge ▫$\{g, g'\}$▫ of ▫$G▫$ there is an edge between copies ▫$gH$▫ and ▫$g'H$▫ of form ▫$\{(g, f(g'), (g', f(g))\}$▫. Some basic properties of the Sierpiński product are presented. In particular, we show that the graph ▫$G\otimes_f H$▫ is connected if and only if both graphs ▫$G$▫ and ▫$H$▫ are connected and we present some conditions that ▫$G, \, H$▫ must fulfill for ▫$G\otimes_f H$▫ to be planar. As for symmetry properties, we show which automorphisms of ▫$G$▫ and ▫$H$▫ extend to automorphisms of ▫$G\otimes_f H$▫. In several cases we can also describe the whole automorphism group of the graph ▫$G\otimes_f H$▫. Finally, we show how to extend the Sierpiński product to multiple factors in a natural way. By applying this operation ▫$n$▫ times to the same graph we obtain an alternative approach to the well-known ▫$n$▫-th generalized Sierpiński graph.
Ključne besede: Sierpiński graphs, graph products, connectivity, planarity, symmetry
Objavljeno v RUP: 06.11.2023; Ogledov: 968; Prenosov: 4
Celotno besedilo (526,44 KB)

Ključne besede: (un)directed Cayley graph, cyclic group, (un)directed circulant graph, Cayley isomorphism, (un)directed CI-graph, (D)CI-group, m-(D)CI-group, key, generalised multiplier
Objavljeno v RUP: 11.09.2023; Ogledov: 1143; Prenosov: 18
Celotno besedilo (520,27 KB)

Ključne besede: distance-regularized vertex, pseudo-distance-regularized vertex, Terwilliger algebra, irreducible module, distance-balanced graph, nicely distance-balanced graph, strongly distance-balanced graph
Objavljeno v RUP: 15.02.2023; Ogledov: 2251; Prenosov: 109
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