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Wyświetlanie 1-15 z 66
Tytuł:
The crossing numbers of certain Cartesian products
Autorzy:
Klešč, Marián
Powiązania:
https://bibliotekanauki.pl/articles/971930.pdf
Data publikacji:
1995
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
drawing
crossing number
path
Cartesian product
Opis:
In this article we determine the crossing numbers of the Cartesian products of given three graphs on five vertices with paths.
Źródło:
Discussiones Mathematicae Graph Theory; 1995, 15, 1; 5-10
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Vizings conjecture and the one-half argument
Autorzy:
Hartnell, Bert
Rall, Douglas
Powiązania:
https://bibliotekanauki.pl/articles/972044.pdf
Data publikacji:
1995
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination number
Cartesian product
Vizing's conjecture
clique
Opis:
The domination number of a graph G is the smallest order, γ(G), of a dominating set for G. A conjecture of V. G. Vizing [5] states that for every pair of graphs G and H, γ(G☐H) ≥ γ(G)γ(H), where G☐H denotes the Cartesian product of G and H. We show that if the vertex set of G can be partitioned in a certain way then the above inequality holds for every graph H. The class of graphs G which have this type of partitioning includes those whose 2-packing number is no smaller than γ(G)-1 as well as the collection of graphs considered by Barcalkin and German in [1]. A crucial part of the proof depends on the well-known fact that the domination number of any connected graph of order at least two is no more than half its order.
Źródło:
Discussiones Mathematicae Graph Theory; 1995, 15, 2; 205-216
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The crossing numbers of products of a 5-vertex graph with paths and cycles
Autorzy:
Klešč, Marián
Powiązania:
https://bibliotekanauki.pl/articles/744243.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
drawing
crossing number
path
cycle
Cartesian product
Opis:
There are several known exact results on the crossing numbers of Cartesian products of paths, cycles or stars with "small" graphs. Let H be the 5-vertex graph defined from K₅ by removing three edges incident with a common vertex. In this paper, we extend the earlier results to the Cartesian products of H × Pₙ and H × Cₙ, showing that in the general case the corresponding crossing numbers are 3n-1, and 3n for even n or 3n+1 if n is odd.
Źródło:
Discussiones Mathematicae Graph Theory; 1999, 19, 1; 59-69
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Recognizing weighted directed cartesian graph bundles
Autorzy:
Zmazek, Blaz
Zerovnik, Janez
Powiązania:
https://bibliotekanauki.pl/articles/743682.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph bundles
Cartesian graph product
weighted digraphs
half-convexity
Opis:
In this paper we show that methods for recognizing Cartesian graph bundles can be generalized to weighted digraphs. The main result is an algorithm which lists the sets of degenerate arcs for all representations of digraph as a weighted directed Cartesian graph bundle over simple base digraphs not containing transitive tournament on three vertices. Two main notions are used. The first one is the new relation $^→δ*$defined among the arcs of a digraph as a weighted directed analogue of the well-known relation δ*. The second one is the concept of half-convex subgraphs. A subgraph H is half-convex in G if any vertex x ∈ G∖H has at most one predecessor and at most one successor.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 1; 39-56
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Vizings conjecture
Autorzy:
Bresar, Bostjan
Powiązania:
https://bibliotekanauki.pl/articles/743820.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
Cartesian product
domination number
Opis:
A dominating set D for a graph G is a subset of V(G) such that any vertex in V(G)-D has a neighbor in D, and a domination number γ(G) is the size of a minimum dominating set for G. For the Cartesian product G ⃞ H Vizing's conjecture [10] states that γ(G ⃞ H) ≥ γ(G)γ(H) for every pair of graphs G,H. In this paper we introduce a new concept which extends the ordinary domination of graphs, and prove that the conjecture holds when γ(G) = γ(H) = 3.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 1; 5-11
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Improving some bounds for dominating Cartesian products
Autorzy:
Hartnell, Bert
Rall, Douglas
Powiązania:
https://bibliotekanauki.pl/articles/743158.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination number
Cartesian product
Vizing's conjecture
2-packing
Opis:
The study of domination in Cartesian products has received its main motivation from attempts to settle a conjecture made by V.G. Vizing in 1968. He conjectured that γ(G)γ(H) is a lower bound for the domination number of the Cartesian product of any two graphs G and H. Most of the progress on settling this conjecture has been limited to verifying the conjectured lower bound if one of the graphs has a certain structural property. In addition, a number of authors have established bounds for dominating the Cartesian product of any two graphs. We show how it is possible to improve some of these bounds by imposing conditions on both graphs. For example, we establish a new lower bound for the domination number of T T, when T is a tree, and we improve an upper bound of Vizing in the case when one of the graphs has k > 1 dominating sets which cover the vertex set and the other has a dominating set which partitions in a certain way.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 2; 261-272
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weak k-reconstruction of Cartesian products
Autorzy:
Imrich, Wilfried
Zmazek, Blaz
Zerovnik, Janez
Powiązania:
https://bibliotekanauki.pl/articles/743162.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
reconstruction problem
Cartesian product
composite graphs
Opis:
By Ulam's conjecture every finite graph G can be reconstructed from its deck of vertex deleted subgraphs. The conjecture is still open, but many special cases have been settled. In particular, one can reconstruct Cartesian products. We consider the case of k-vertex deleted subgraphs of Cartesian products, and prove that one can decide whether a graph H is a k-vertex deleted subgraph of a Cartesian product G with at least k+1 prime factors on at least k+1 vertices each, and that H uniquely determines G. This extends previous work of the authors and Sims. The paper also contains a counterexample to a conjecture of MacAvaney.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 2; 273-285
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On dominating the Cartesian product of a graph and K₂
Autorzy:
Hartnell, Bert
Rall, Douglas
Powiązania:
https://bibliotekanauki.pl/articles/744535.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
2-packing, Cartesian product
Opis:
In this paper we consider the Cartesian product of an arbitrary graph and a complete graph of order two. Although an upper and lower bound for the domination number of this product follow easily from known results, we are interested in the graphs that actually attain these bounds. In each case, we provide an infinite class of graphs to show that the bound is sharp. The graphs that achieve the lower bound are of particular interest given the special nature of their dominating sets and are investigated further.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 3; 389-402
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Categories of functors between categories with partial morphisms
Autorzy:
Vogel, Hans-Jürgen
Powiązania:
https://bibliotekanauki.pl/articles/729097.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
symmetric monoidal category
dhts-category
Hoehnke category
Hoehnke theory
monoidal functor
d-monoidal functor
dht-symmetric functor
functor composition
cartesian product
Opis:
It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 1; 39-87
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Note on the split domination number of the Cartesian product of paths
Autorzy:
Zwierzchowski, Maciej
Powiązania:
https://bibliotekanauki.pl/articles/744304.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination number
split domination number
Cartesian product of graphs
Opis:
In this note the split domination number of the Cartesian product of two paths is considered. Our results are related to [2] where the domination number of Pₘ ☐ Pₙ was studied. The split domination number of P₂ ☐ Pₙ is calculated, and we give good estimates for the split domination number of Pₘ ☐ Pₙ expressed in terms of its domination number.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 79-84
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some crossing numbers of products of cycles
Autorzy:
Klešč, Marián
Powiązania:
https://bibliotekanauki.pl/articles/744339.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
drawing
crossing number
cycle
Cartesian product
Opis:
The exact values of crossing numbers of the Cartesian products of four special graphs of order five with cycles are given and, in addition, all known crossing numbers of Cartesian products of cycles with connected graphs on five vertices are summarized.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 197-210
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Defining sets in (proper) vertex colorings of the Cartesian product of a cycle with a complete graph
Autorzy:
Mojdeh, D.
Powiązania:
https://bibliotekanauki.pl/articles/743869.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph coloring
defining set
cartesian product
Opis:
In a given graph G = (V,E), a set of vertices S with an assignment of colors to them is said to be a defining set of the vertex coloring of G, if there exists a unique extension of the colors of S to a c ≥ χ(G) coloring of the vertices of G. A defining set with minimum cardinality is called a minimum defining set and its cardinality is the defining number, denoted by d(G,c).
The d(G = Cₘ × Kₙ, χ(G)) has been studied. In this note we show that the exact value of defining number d(G = Cₘ × Kₙ, c) with c > χ(G), where n ≥ 2 and m ≥ 3, unless the defining number $d(K₃×C_{2r},4)$, which is given an upper and lower bounds for this defining number. Also some bounds of defining number are introduced.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 1; 59-72
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graphs with convex domination number close to their order
Autorzy:
Cyman, Joanna
Lemańska, Magdalena
Raczek, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/743979.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
convex domination
Cartesian product
Opis:
For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance $d_G(u,v)$ between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length $d_G(u,v)$ is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number $γ_{con}(G)$ of a graph G is the minimum cardinality of a convex dominating set in G. Graphs with the convex domination number close to their order are studied. The convex domination number of a Cartesian product of graphs is also considered.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 2; 307-316
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Grundy number of graphs
Autorzy:
Effantin, Brice
Kheddouci, Hamamache
Powiązania:
https://bibliotekanauki.pl/articles/743619.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Grundy coloring
vertex coloring
cartesian product
graph product
Opis:
The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex x colored with color i, 1 ≤ i ≤ k, is adjacent to (i-1) vertices colored with each color j, 1 ≤ j ≤ i -1. In this paper we give bounds for the Grundy number of some graphs and cartesian products of graphs. In particular, we determine an exact value of this parameter for n-dimensional meshes and some n-dimensional toroidal meshes. Finally, we present an algorithm to generate all graphs for a given Grundy number.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 1; 5-18
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On θ-graphs of partial cubes
Autorzy:
Klavžar, Sandi
Kovse, Matjaz
Powiązania:
https://bibliotekanauki.pl/articles/743784.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
intersection graph
partial cube
median graph
expansion theorem
Cartesian product of graphs
Opis:
The Θ-graph Θ(G) of a partial cube G is the intersection graph of the equivalence classes of the Djoković-Winkler relation. Θ-graphs that are 2-connected, trees, or complete graphs are characterized. In particular, Θ(G) is complete if and only if G can be obtained from K₁ by a sequence of (newly introduced) dense expansions. Θ-graphs are also compared with familiar concepts of crossing graphs and τ-graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 2; 313-321
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 66

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