Temat: Cartesian product - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Graphs with convex domination number close to their order
Autorzy:: Cyman, Joanna
Lemańska, Magdalena
Raczek, Joanna
Tematy:: convex domination
Cartesian product; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743979.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Separation of Cartesian Products of Graphs Into Several Connected Components by the Removal of Vertices
Autorzy:: Erker, Tjaša Paj
Špacapan, Simon
Tematy:: k -connectivity
Cartesian product; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32304144.pdf Link otwiera się w nowym oknie
Opis:: A set S ⊆ V (G) is a vertex k-cut in a graph G = (V (G), E(G)) if G − S has at least k connected components. The k-connectivity of G, denoted as κ_k(G), is the minimum cardinality of a vertex k-cut in G. We give several constructions of a set S such that (G□H) − S has at least three connected components. Then we prove that for any 2-connected graphs G and H, of order at least six, one of the defined sets S is a minimum vertex 3-cut in G□H. This yields a formula for κ₃(G□H).
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: On Vizings conjecture
Autorzy:: Bresar, Bostjan
Tematy:: graph
Cartesian product
domination number; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743820.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: On dominating the Cartesian product of a graph and K₂
Autorzy:: Hartnell, Bert
Rall, Douglas
Tematy:: domination
2-packing, Cartesian product; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/744535.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: The Thickness of Amalgamations and Cartesian Product of Graphs
Autorzy:: Yang, Yan
Chen, Yichao
Tematy:: thickness
amalgamation
Cartesian product
genus; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31341728.pdf Link otwiera się w nowym oknie
Opis:: The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product K_n □ P_m for most values of m and n.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: The Crossing Number of Cartesian Product of 5-Wheel with any Tree
Autorzy:: Wang, Yuxi
Huang, Yuanqiu
Tematy:: drawing
crossing number
join product
Cartesian product; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32083823.pdf Link otwiera się w nowym oknie
Opis:: In this paper, we establish the crossing number of join product of 5-wheel with n isolated vertices. In addition, the exact values for the crossing numbers of Cartesian products of the wheels of order at most five with any tree T are given.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: On the Crossing Numbers of Cartesian Products of Wheels and Trees
Autorzy:: Klešč, Marián
Petrillová, Jana
Valo, Matúš
Tematy:: graph
drawing
crossing number
join product
Cartesian product; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31341838.pdf Link otwiera się w nowym oknie
Opis:: Bokal developed an innovative method for finding the crossing numbers of Cartesian product of two arbitrarily large graphs. In this article, the crossing number of the join product of stars and cycles are given. Afterwards, using Bokal’s zip product operation, the crossing numbers of the Cartesian products of the wheel W_n and all trees T with maximum degree at most five are established.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: The domination number of $K_n^3$
Autorzy:: Georges, John
Lin, Jianwei
Mauro, David
Tematy:: Cartesian product
dominating set
domination number; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/30148694.pdf Link otwiera się w nowym oknie
Opis:: Let $K_n^3$ denote the Cartesian product $K_n□K_n□K_n$, where $K_n$ is the complete graph on $n$ vertices. We show that the domination number of $K_n^3$ is $⌈\frac{n^2}{2}⌉$.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: The metric dimension of circulant graphs and their Cartesian products
Autorzy:: Chau, K.
Gosselin, S.
Tematy:: metric dimension
circulant graph
Cartesian product; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255804.pdf Link otwiera się w nowym oknie
Opis:: Let G = (V, E) be a connected graph (or hypergraph) and let d(x,y) denote the distance between vertices x,y ∈V(G). A subset W ⊆V(G) is called a resolving set for G if for every pair ol distinct vertices x, y ∈ (G), there is w ∈W such that d(x,w) ≠d(y,w). The minimum cardinality of a resolving set for G is called the metric dimension of G, denoted by β (G). The circulant graph Cn(l, 2,... , t) has vertex set {v0, v1 …, vn-1} and edges [formula] where 0 ≤ i ≤ n — 1 and 1 ≤j ≤ t and the indices are taken modulo [formula]. In this paper we determine the exact metric dimension olthe circulant graphs Cn(l, 2,... , t). extending previous results due to Borchert and Gosselin (2013), Grigorious et al. (2014), and Vetrik (2016). In particular, we show that [formula] for large enough n, which implies that the metric dimension ol these circulants is completely determined by the congruence class ol n modulo 2t. We determine the exact value of β Cn (l, 2,.. . , i)) for n ≡ 2 mod 2t and n =≡ (t + 1) mod 2t and we give better bounds on the metric dimension ol these circulants for n ≡ 0 mod 2t and n ≡ 1 mod 2t. In addition, we bound the metric dimension ol Cartesian products ol circulant graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: Weak k-reconstruction of Cartesian products
Autorzy:: Imrich, Wilfried
Zmazek, Blaz
Zerovnik, Janez
Tematy:: reconstruction problem
Cartesian product
composite graphs; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743162.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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