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    Wyświetlanie 1-8 z 8
    Tytuł:
    γ-graphs of graphs
    Autorzy:
    Fricke, Gerd
    Hedetniemi, Sandra
    Hedetniemi, Stephen
    Hutson, Kevin
    Powiązania:
    https://bibliotekanauki.pl/articles/743973.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    dominating sets
    gamma graphs
    Opis:
    A set S ⊆ V is a dominating set of a graph G = (V,E) if every vertex in V -S is adjacent to at least one vertex in S. The domination number γ(G) of G equals the minimum cardinality of a dominating set S in G; we say that such a set S is a γ-set. In this paper we consider the family of all γ-sets in a graph G and we define the γ-graph G(γ) = (V(γ), E(γ)) of G to be the graph whose vertices V(γ) correspond 1-to-1 with the γ-sets of G, and two γ-sets, say D₁ and D₂, are adjacent in E(γ) if there exists a vertex v ∈ D₁ and a vertex w ∈ D₂ such that v is adjacent to w and D₁ = D₂ - {w} ∪ {v}, or equivalently, D₂ = D₁ - {v} ∪ {w}. In this paper we initiate the study of γ-graphs of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 3; 517-531
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convex universal fixers
    Autorzy:
    Lemańska, Magdalena
    Zuazua, Rita
    Powiązania:
    https://bibliotekanauki.pl/articles/743272.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    convex sets
    dominating sets
    universal fixers
    Opis:
    In [1] Burger and Mynhardt introduced the idea of universal fixers. Let G = (V, E) be a graph with n vertices and G' a copy of G. For a bijective function π: V(G) → V(G'), define the prism πG of G as follows: V(πG) = V(G) ∪ V(G') and $E(πG) = E(G) ∪ E(G') ∪ M_{π}$, where $M_{π} = {u π(u) | u ∈ V(G)}$. Let γ(G) be the domination number of G. If γ(πG) = γ(G) for any bijective function π, then G is called a universal fixer. In [9] it is conjectured that the only universal fixers are the edgeless graphs K̅ₙ. In this work we generalize the concept of universal fixers to the convex universal fixers. In the second section we give a characterization for convex universal fixers (Theorem 6) and finally, we give an in infinite family of convex universal fixers for an arbitrary natural number n ≥ 10.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 4; 807-812
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nearly perfect sets in the n-fold products of graphs
    Autorzy:
    Perl, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255571.pdf
    Data publikacji:
    2007
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    dominating sets
    product of graphs
    Opis:
    The study of nearly perfect sets in graphs was initiated in [2], Let S ⊆ V(G). We say that S is a nearly perfect set (or is nearly perfect) in G if every vertex in V(G) - S is adjacent to at most one vertex in S. A nearly perfect set S in G is called 1-maximal if for every vertex u ∈ V(G) - S, S ∪ {u} is not nearly perfect in G. We denote the minimum cardinality of a 1-maximal nearly perfect set in G by np(G). We will call the 1-maximal nearly perfect set of the cardinality np(G) an np(G) - set. In this paper, we evaluate the parameter np(G) for some n-fold products of graphs. To this effect, we determine 1-maximal nearly perfect sets in the n-fold Cartesian product of graphs and in the n-fold strong product of graphs.
    Źródło:
    Opuscula Mathematica; 2007, 27, 1; 83-88
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A note on Vizings generalized conjecture
    Autorzy:
    Blidia, M.
    Chellali, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255435.pdf
    Data publikacji:
    2007
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    graph
    dominating sets
    Vizing's conjecture
    Opis:
    In this note we give a generalized version of Vizing's conjecture concerning the distance domination number for the cartesian product of two graphs.
    Źródło:
    Opuscula Mathematica; 2007, 27, 2; 181-185
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nearly perfect sets in products of graphs
    Autorzy:
    Kwaśnik, M.
    Perl, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/2050769.pdf
    Data publikacji:
    2004
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    dominating sets
    product of graphs
    Opis:
    The study of nearly perfect sets in graphs was initiated in [2]. Let $S \subseteq V(G)$. We say that $S$ is a nearly perfect set (or is nearly perfect) in $G$ if every vertex in $V(G) - S$ is adjacent to at most one vertex in $S$. A nearly perfect set $S$ in $G$ is called maximal if for every vertex $u \in V(G) - S, S \cup \{u\}$ is not nearly perfect in $G$. The minimum cardinality of a maximal nearly perfect set is denoted by $n_{p}(G)$. It is our purpose in this paper to determine maximal nearly perfect sets in two well-known products of two graphs, i.e. in the Cartesian product and in the strong product. Lastly, we give upper bounds of $n_{p}(G1 \times G2)$ and $n_{p}(G1 \otimes G2)$, for some special graphs $G1,G2$.
    Źródło:
    Opuscula Mathematica; 2004, 24, 2; 177-180
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lattice-Like Total Perfect Codes
    Autorzy:
    Araujo, Carlos
    Dejter, Italo
    Powiązania:
    https://bibliotekanauki.pl/articles/30147219.pdf
    Data publikacji:
    2014-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    perfect dominating sets
    hypercubes
    lattices
    Opis:
    A contribution is made to the classification of lattice-like total perfect codes in integer lattices $Λ_n$ via pairs ($G, Φ$) formed by abelian groups $G$ and homomorphisms $Φ: Z^n → G$. A conjecture is posed that the cited contribution covers all possible cases. A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in $Λ_n$ with induced components that are parallel paths of length > 1 is posed as well.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 1; 57-74
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Open Locating-Dominating Sets in Circulant Graphs
    Autorzy:
    Givens, Robin M.
    Yu, Gexin
    Kincaid, Rex K.
    Powiązania:
    https://bibliotekanauki.pl/articles/32361753.pdf
    Data publikacji:
    2022-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    open locating-dominating sets
    circulant graphs
    Hall’s Matching Theorem
    mixed-weight open locating-dominating sets
    Opis:
    Location detection problems have been studied for a variety of applications including finding faults in multiprocessors, contaminants in public utilities, intruders in buildings and facilities, and for environmental monitoring using wireless sensor networks. In each of these applications, the system or structure can be modeled as a graph, and sensors placed strategically at a subset of vertices can locate and detect anomalies in the system. An open locating-dominating set (OLD-set) is a subset of vertices in a graph in which every vertex in the graph has a non-empty and unique set of neighbors in the subset. Sensors placed at OLD-set vertices can uniquely detect and locate disturbances in a system. These sensors can be expensive and, as a result, minimizing the size of the OLD-set is critical. Circulant graphs, a group of regular cyclic graphs, are often used to model parallel networks. We prove the optimal OLD-set size for a particular circulant graph using Hall’s Theorem. We also consider the mixed-weight OLD-set introduced in [R.M. Givens, R.K. Kincaid, W. Mao and G. Yu, Mixed-weight open locating-dominating sets, in: 2017 Annual Conference on Information Science and Systems, (IEEE, Baltimor, 2017) 1–6] which models a system with sensors of varying strengths. To model these systems, we place weights on the vertices in the graph, representing the strength of a sensor placed at the corresponding location in the system. We study particular mixed-weight OLD-sets in cycles, which behave similarly to OLD-sets in circulant graphs, and show the optimal mixed-weight OLD-set size using the discharging method.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 1; 47-62
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fault Tolerant Detectors for Distinguishing Sets in Graphs
    Autorzy:
    Seo, Suk J.
    Slater, Peter J.
    Powiązania:
    https://bibliotekanauki.pl/articles/31234046.pdf
    Data publikacji:
    2015-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    distinguishing sets
    fault tolerant detectors
    redundant distinguishing open-locating-dominating set
    detection distinguishing open-locating-dominating set
    Opis:
    For various domination-related parameters involving locating devices (distinguishing sets) that function as places from which detectors can determine information about the location of an “intruder”, several types of possible detector faults are identified. Two of these fault tolerant detector types for distinguishing sets are considered here, namely redundant distinguishing and detection distinguishing. Illustrating these concepts, we focus primarily on open-locating-dominating sets.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2015, 35, 4; 797-818
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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