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Wyświetlanie 1-15 z 26
Tytuł:
Maximum Independent Sets in Direct Products of Cycles or Trees with Arbitrary Graphs
Autorzy:
Paj, Tjaša
Špacapan, Simon
Powiązania:
https://bibliotekanauki.pl/articles/31339257.pdf
Data publikacji:
2015-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
direct product
independent set
Opis:
The direct product of graphs G = (V (G), E(G)) and H = (V (H), E(H)) is the graph, denoted as G×H, with vertex set V (G×H) = V (G)×V (H), where vertices (x1, y1) and (x2, y2) are adjacent in G × H if x1x2 ∈ E(G) and y1y2 ∈ E(H). Let n be odd and m even. We prove that every maximum independent set in Pn×G, respectively Cm×G, is of the form (A×C)∪(B×D), where C and D are nonadjacent in G, and A∪B is the bipartition of Pn respectively Cm. We also give a characterization of maximum independent subsets of Pn × G for every even n and discuss the structure of maximum independent sets in T × G where T is a tree.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 4; 675-688
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cancellation of direct products of digraphs
Autorzy:
Hammack, Richard
Toman, Katherine
Powiązania:
https://bibliotekanauki.pl/articles/744073.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph direct product
graph product cancellation
digraphs
Opis:
We investigate expressions of form A×C ≅ B×C involving direct products of digraphs. Lovász gave exact conditions on C for which it necessarily follows that A ≅ B. We are here concerned with a different aspect of cancellation. We describe exact conditions on A for which it necessarily follows that A ≅ B. In the process, we do the following: Given an arbitrary digraph A and a digraph C that admits a homomorphism onto an arc, we classify all digraphs B for which A×C ≅ B×C.
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 4; 575-590
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Isomorphic components of direct products of bipartite graphs
Autorzy:
Hammack, Richard
Powiązania:
https://bibliotekanauki.pl/articles/743937.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
direct product
tensor product
Kronecker product
bipartite graph
Opis:
A standard result states the direct product of two connected bipartite graphs has exactly two components. Jha, Klavžar and Zmazek proved that if one of the factors admits an automorphism that interchanges partite sets, then the components are isomorphic. They conjectured the converse to be true. We prove the converse holds if the factors are square-free. Further, we present a matrix-theoretic conjecture that, if proved, would prove the general case of the converse; if refuted, it would produce a counterexample.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 2; 231-248
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A cancellation property for the direct product of graphs
Autorzy:
Hammack, Richard
Powiązania:
https://bibliotekanauki.pl/articles/743303.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph products
graph direct product
cancellation
Opis:
Given graphs A, B and C for which A×C ≅ B×C, it is not generally true that A ≅ B. However, it is known that A×C ≅ B×C implies A ≅ B provided that C is non-bipartite, or that there are homomorphisms from A and B to C. This note proves an additional cancellation property. We show that if B and C are bipartite, then A×C ≅ B×C implies A ≅ B if and only if no component of B admits an involution that interchanges its partite sets.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 1; 179-184
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Centers of n-fold tensor products of graphs
Autorzy:
Bendall, Sarah
Hammack, Richard
Powiązania:
https://bibliotekanauki.pl/articles/744586.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph tensor product
graphs direct product
graph center
Opis:
Formulas for vertex eccentricity and radius for the n-fold tensor product $G = ⊗_{i=1} ⁿG_i$ of n arbitrary simple graphs $G_i$ are derived. The center of G is characterized as the union of n+1 vertex sets of form V₁×V₂×...×Vₙ, with $V_i ⊆ V(G_i)$.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 3; 491-501
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
2-Tone Colorings in Graph Products
Autorzy:
Loe, Jennifer
Middelbrooks, Danielle
Morris, Ashley
Wash, Kirsti
Powiązania:
https://bibliotekanauki.pl/articles/31339114.pdf
Data publikacji:
2015-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
t-tone coloring
Cartesian product
direct product
strong product
Opis:
A variation of graph coloring known as a t-tone k-coloring assigns a set of t colors to each vertex of a graph from the set {1, . . ., k}, where the sets of colors assigned to any two vertices distance d apart share fewer than d colors in common. The minimum integer k such that a graph G has a t- tone k-coloring is known as the t-tone chromatic number. We study the 2-tone chromatic number in three different graph products. In particular, given graphs G and H, we bound the 2-tone chromatic number for the direct product G×H, the Cartesian product G□H, and the strong product G⊠H.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 1; 55-72
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On 3-Colorings of Direct Products of Graphs
Autorzy:
Špacapan, Simon
Powiązania:
https://bibliotekanauki.pl/articles/31343446.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
independence number
direct product
Hedetniemi’s conjecture
Opis:
The k-independence number of a graph G, denoted as αk(G), is the order of a largest induced k-colorable subgraph of G. In [S. Špacapan, The k-independence number of direct products of graphs, European J. Combin. 32 (2011) 1377–1383] the author conjectured that the direct product G × H of graphs G and H obeys the following bound αk(G×H)≤αk(G)|V(H)|+αk(H)|V(G)|−αk(G)αk(H), and proved the conjecture for k = 1 and k = 2. If true for k = 3 the conjecture strenghtens the result of El-Zahar and Sauer who proved that any direct product of 4-chromatic graphs is 4-chromatic [M. El-Zahar and N. Sauer, The chromatic number of the product of two 4-chromatic graphs is 4, Combinatorica 5 (1985) 121–126]. In this paper we prove that the above bound is true for k = 3 provided that G and H are graphs that have complete tripartite subgraphs of orders α3(G) and α3(H), respectively.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 391-413
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Proper Connection Of Direct Products
Autorzy:
Hammack, Richard H.
Taylor, Dewey T.
Powiązania:
https://bibliotekanauki.pl/articles/31341584.pdf
Data publikacji:
2017-11-27
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
direct product of graphs
proper connection of graphs
Opis:
The proper connection number of a graph is the least integer k for which the graph has an edge coloring with k colors, with the property that any two vertices are joined by a properly colored path. We prove that given two connected non-bipartite graphs, one of which is (vertex) 2-connected, the proper connection number of their direct product is 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 4; 1005-1013
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On acyclic colorings of direct products
Autorzy:
Špacapan, Simon
Horvat, Aleksandra
Powiązania:
https://bibliotekanauki.pl/articles/743326.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
coloring
acyclic coloring
distance-two coloring
direct product
Opis:
A coloring of a graph G is an acyclic coloring if the union of any two color classes induces a forest. It is proved that the acyclic chromatic number of direct product of two trees T₁ and T₂ equals min{Δ(T₁) + 1, Δ(T₂) + 1}. We also prove that the acyclic chromatic number of direct product of two complete graphs Kₘ and Kₙ is mn-m-2, where m ≥ n ≥ 4. Several bounds for the acyclic chromatic number of direct products are given and in connection to this some questions are raised.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 2; 323-333
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Well-Covered Direct Products
Autorzy:
Kuenzel, Kirsti
Rall, Douglas F.
Powiązania:
https://bibliotekanauki.pl/articles/32315158.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
well-covered graph
direct product of graphs
isolatable vertex
Opis:
A graph G is well-covered if all maximal independent sets of G have the same cardinality. In 1992 Topp and Volkmann investigated the structure of well-covered graphs that have nontrivial factorizations with respect to some of the standard graph products. In particular, they showed that both factors of a well-covered direct product are also well-covered and proved that the direct product of two complete graphs (respectively, two cycles) is well-covered precisely when they have the same order (respectively, both have order 3 or 4). Furthermore, they proved that the direct product of two well-covered graphs with independence number one-half their order is well-covered. We initiate a characterization of nontrivial connected well-covered graphs G and H, whose independence numbers are strictly less than one-half their orders, such that their direct product G × H is well-covered. In particular, we show that in this case both G and H have girth 3 and we present several infinite families of such well-covered direct products. Moreover, we show that if G is a factor of any well-covered direct product, then G is a complete graph unless it is possible to create an isolated vertex by removing the closed neighborhood of some independent set of vertices in G.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 627-640
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some results on total domination in direct products of graphs
Autorzy:
Dorbec, Paul
Gravier, Sylvain
Klavžar, Sandi
Spacapan, Simon
Powiązania:
https://bibliotekanauki.pl/articles/743885.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
direct product
total domination
k-tuple domination
open packing
domination
Opis:
Upper and lower bounds on the total domination number of the direct product of graphs are given. The bounds involve the {2}-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direct products of graphs is also bounded from below.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 1; 103-112
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Median and quasi-median direct products of graphs
Autorzy:
Brešar, Boštjan
Jha, Pranava
Klavžar, Sandi
Zmazek, Blaž
Powiązania:
https://bibliotekanauki.pl/articles/744332.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
median graph
direct product
quasi-median graph
isometric embeddings
convexity
Opis:
Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G×P₃ is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G×K₂ are proved, and it is shown that the only nonbipartite quasi-median direct product is K₃×K₃.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 183-196
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adjacent vertex distinguishing edge colorings of the direct product of a regular graph by a path or a cycle
Autorzy:
Frigerio, Laura
Lastaria, Federico
Salvi, Norma
Powiązania:
https://bibliotekanauki.pl/articles/743981.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
chromatic index
adjacent vertex distinguishing edge coloring
direct product
matching
Opis:
In this paper we investigate the minimum number of colors required for a proper edge coloring of a finite, undirected, regular graph G in which no two adjacent vertices are incident to edges colored with the same set of colors. In particular, we study this parameter in relation to the direct product of G by a path or a cycle.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 3; 547-557
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An ideal-based zero-divisor graph of direct products of commutative rings
Autorzy:
Atani, S.
Kohan, M.
Sarvandi, Z.
Powiązania:
https://bibliotekanauki.pl/articles/729207.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
zero-divisor graph
ideal-based
diameter
girth
finite direct product
Opis:
In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2014, 34, 1; 45-53
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new proof of a theorem of Balcerzyk, Białynicki-Birula and Łoś
Autorzy:
O'Neill, John
Powiązania:
https://bibliotekanauki.pl/articles/966849.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
measurable cardinal number
abelian group
torsion-free
direct product
slender group
Źródło:
Colloquium Mathematicum; 1996, 70, 2; 191-194
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 26

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