Informacja

Drogi użytkowniku, aplikacja do prawidłowego działania wymaga obsługi JavaScript. Proszę włącz obsługę JavaScript w Twojej przeglądarce.

English (EN)·Polski (PL)·Yкраїнський (UK)
Przejdź do strony domowej biblioteki Centralna Biblioteka Wojskowa Link otwiera się w nowym oknie Logo biblioteki Prolib Integro - strona głównaCentralna Biblioteka Wojskowa

Wyszukujesz frazę "signed dominating function" wg kryterium: Temat

  Lista filtrów
Wyrównaj
    Wyświetlanie 1-12 z 12
    Tytuł:
    Signed domination and signed domatic numbers of digraphs
    Autorzy:
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/743935.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    digraph
    oriented graph
    signed dominating function
    signed domination number
    signed domatic number
    Opis:
    Let D be a finite and simple digraph with the vertex set V(D), and let f:V(D) → {-1,1} be a two-valued function. If $∑_{x ∈ N¯[v]}f(x) ≥ 1$ for each v ∈ V(D), where N¯[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V(D)) is called the weight w(f) of f. The minimum of weights w(f), taken over all signed dominating functions f on D, is the signed domination number $γ_S(D)$ of D. A set ${f₁,f₂,...,f_d}$ of signed dominating functions on D with the property that $∑_{i = 1}^d f_i(x) ≤ 1$ for each x ∈ V(D), is called a signed dominating family (of functions) on D. The maximum number of functions in a signed dominating family on D is the signed domatic number of D, denoted by $d_S(D)$. In this work we show that $4-n ≤ γ_S(D) ≤ n$ for each digraph D of order n ≥ 2, and we characterize the digraphs attending the lower bound as well as the upper bound. Furthermore, we prove that $γ_S(D) + d_S(D) ≤ n + 1$ for any digraph D of order n, and we characterize the digraphs D with $γ_S(D) + d_S(D) = n + 1$. Some of our theorems imply well-known results on the signed domination number of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 3; 415-427
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bounds on the inverse signed total domination numbers in graphs
    Autorzy:
    Atapour, M.
    Norouzian, S.
    Sheikholeslami, S. M.
    Volkmann, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/255596.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    inverse signed total dominating function
    inverse signed total domination number
    Opis:
    Let G = (V, E) be a simple graph. A function ƒ : V→ {- 1,1} is called an inverse signed total dominating function if the sum of its function values over any open neighborhood is at most zero. The inverse signed total domination number of G, denoted by [formula], equals to the maximum weight of an inverse signed total dominating function of G. In this paper, we establish upper bounds on the inverse signed total domination number of graphs in terms of their order, size and maximum and minimum degrees.
    Źródło:
    Opuscula Mathematica; 2016, 36, 2; 145-152
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On signed arc total domination in digraphs
    Autorzy:
    Asgharsharghi, L.
    Khodkar, A.
    Sheikholeslami, S. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/254811.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    signed arc total dominating function signed arc total domination number domination in digraphs
    Opis:
    Let D = (V, A) be a finite simple digraph and N(uv) = {u'v' ≠ uv | u = u' or v = v'} be the open neighbourhood of uv in D. A function ƒ : A → { — 1, +1} is said to be a signed arc total dominating function (SATDF) of D if [formula] holds for every arc uv ∈ A. The signed arc total domination number [formula] is defined as [formula]. In this paper we initiate the study of the signed arc total domination in digraphs and present some lower bounds for this parameter.
    Źródło:
    Opuscula Mathematica; 2018, 38, 6; 779-794
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak signed Roman k-domination in digraphs
    Autorzy:
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/29519480.pdf
    Data publikacji:
    2024
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    digraph
    weak signed Roman k-dominating function
    weak signed Roman k-domination number
    signed Roman k-dominating function
    signed Roman k-domination number
    Opis:
    Let $ k ≥ 1 $ be an integer, and let $ D $ be a finite and simple digraph with vertex set $ V (D) $. A weak signed Roman k-dominating function (WSRkDF) on a digraph $ D $ is a function $ f : V (D) → {−1, 1, 2} $ satisfying the condition that $ \Sigma_{x∈N^−[v]} f(x) ≥ k $ for each v ∈ V (D), where $ N^− [v] $ consists of $ v $ and all vertices of $ D $ from which arcs go into $ v $. The weight of a WSRkDF $ f $ is $ w(f) = \Sigma_{v∈V} (D) f(v) $. The weak signed Roman k-domination number $ \gamma_{wsR}^k (D) $ is the minimum weight of a WSRkDF on $ D $. In this paper we initiate the study of the weak signed Roman k-domination number of digraphs, and we present different bounds on $ \gamma_{wsR}^k (D) $. In addition, we determine the weak signed Roman k-domination number of some classes of digraphs. Some of our results are extensions of well-known properties of the weak signed Roman domination number $ \gamma_{wsR} (D) = \gamma_{wsR}^1 (D) $ and the signed Roman k-domination number $ \gamma_{sR}^k (D) $.
    Źródło:
    Opuscula Mathematica; 2024, 44, 2; 285-296
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Signed Total Roman Edge Domination In Graphs
    Autorzy:
    Asgharsharghi, Leila
    Sheikholeslami, Seyed Mahmoud
    Powiązania:
    https://bibliotekanauki.pl/articles/31341578.pdf
    Data publikacji:
    2017-11-27
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed total Roman dominating function
    signed total Roman domination number
    signed total Roman edge dominating function
    signed total Roman edge domination number
    Opis:
    Let $ G = (V,E) $ be a simple graph with vertex set $V$ and edge set $E$. A signed total Roman edge dominating function of $G$ is a function $ f : E \rightarrow {−1, 1, 2} $ satisfying the conditions that (i) $ \Sigma_{e^′ \in N(e)} f(e^′) \ge 1 $ for each $ e \in E $, where $N(e)$ is the open neighborhood of $e$, and (ii) every edge $e$ for which $f(e) = −1$ is adjacent to at least one edge $ e^′$ for which $f(e^′) = 2$. The weight of a signed total Roman edge dominating function $f$ is $ \omega(f) = \Sigma_{e \in E } f(e) $. The signed total Roman edge domination number $ \gamma_{stR}^' (G) $ of $G$ is the minimum weight of a signed total Roman edge dominating function of $G$. In this paper, we first prove that for every tree $T$ of order $ n \ge 4 $, $ \gamma_{stR}^' (T) \ge \frac{17−2n}{5} $ and we characterize all extreme trees, and then we present some sharp bounds for the signed total Roman edge domination number. We also determine this parameter for some classes of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 4; 1039-1053
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Signed star (k, k)-domatic number of a graph
    Autorzy:
    Sheikholeslami, S. M.
    Volkmann, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/254927.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    signed star (k, k)-domatic number
    signed star domatic number
    signed star k-dominating function
    signed star dominating function
    signed star k-domination number
    signed star domination number
    regular graphs
    Opis:
    Let G be a simple graph without isolated vertices with vertex set V (G) and edge set E(G) and let k be a positive integer. A function ƒ: E(G) →{−1, 1} is said to be a signed star k-dominating function on [formula] for every vertex v of G, where E(v) = {uv ∈ E(G) | u ∈ N(v)}. A set {f1, f2, . . . , fd} of signed star k-dominating functions on G with the property that [formula] for each e ∈ E(G) is called a signed star (k, k)-dominating family (of functions) on G. The maximum number of functions in a signed star (k, k)-dominating family on G is the signed star (k, k)-domatic number of G, denoted by [formula]. In this paper we study properties of the signed star (k, k)-domatic number [formula]. In particular, we present bounds on [formula], and we determine the signed (k, k)-domatic number of some regular graphs. Some of our results extend these given by Atapour, Sheikholeslami, Ghameslou and Volkmann [Signed star domatic number of a graph, Discrete Appl. Math. 158 (2010), 213–218] for the signed star domatic number.
    Źródło:
    Opuscula Mathematica; 2014, 34, 3; 609-620
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Signed Total Roman Domination in Digraphs
    Autorzy:
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31342127.pdf
    Data publikacji:
    2017-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    digraph
    signed total Roman dominating function
    signed total Roman domination number
    Opis:
    Let $D$ be a finite and simple digraph with vertex set $V (D)$. A signed total Roman dominating function (STRDF) on a digraph $D$ is a function $ f : V (D) \rightarrow {−1, 1, 2} $ satisfying the conditions that (i) $ \Sigma_{x \in N^− (v) } f(x) \ge 1 $ for each $ v \in V (D) $, where $ N^− (v) $ consists of all vertices of $D$ from which arcs go into $v$, and (ii) every vertex u for which $f(u) = −1$ has an inner neighbor $v$ for which $f(v) = 2$. The weight of an STRDF $f$ is $ w(f) = \Sigma_{ v \in V } (D) f(v) $. The signed total Roman domination number $ \gamma_{stR} (D) $ of $D$ is the minimum weight of an STRDF on $D$. In this paper we initiate the study of the signed total Roman domination number of digraphs, and we present different bounds on $ \gamma_{stR} (D) $. In addition, we determine the signed total Roman domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman domination number $ \gamma_{stR} (G)$ of graphs $G$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 1; 261-272
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the inverse signed total domination number in graphs
    Autorzy:
    Mojdeh, D. A.
    Samadi, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/255392.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    inverse signed total dominating function
    inverse signed total domination number
    k-tuple total domination number
    Opis:
    In this paper, we study the inverse signed total domination number in graphs and present new sharp lower and upper bounds on this parameter. For example by making use of the classic theorem of Turán (1941), we present a sharp upper bound on Kr+1-free graphs for r ≥ 2. Also, we bound this parameter for a tree from below in terms of its order and the number of leaves and characterize all trees attaining this bound.
    Źródło:
    Opuscula Mathematica; 2017, 37, 3; 447-456
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bounds on the Signed Roman k-Domination Number of a Digraph
    Autorzy:
    Chen, Xiaodan
    Hao, Guoliang
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31343713.pdf
    Data publikacji:
    2019-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed Roman k-dominating function
    signed Roman k-domination number
    digraph
    oriented tree
    Opis:
    Let $k$ be a positive integer. A signed Roman $k$-dominating function (SRkDF) on a digraph $D$ is a function $ f : V (D) \rightarrow \{−1, 1, 2 \} $ satisfying the conditions that (i) $ \Sigma_{ x \in N^− [v] } f(x) \ge k $ for each $ v \in V (D) $, where $ N^− [v] $ is the closed in-neighborhood of $v$, and (ii) each vertex $u$ for which $f(u) = −1$ has an in-neighbor $v$ for which $f(v) = 2$. The weight of an SRkDF $f$ is $ \Sigma_{ v \in V (D) } f(v) $. The signed Roman $k$-domination number $ \gamma_{sR}^k (D) $ of a digraph $D$ is the minimum weight of an SRkDF on $D$. We determine the exact values of the signed Roman $k$-domination number of some special classes of digraphs and establish some bounds on the signed Roman $k$-domination number of general digraphs. In particular, for an oriented tree $T$ of order $n$, we show that $ \gamma_{sR}^2 (T) \ge (n + 3)//2 $, and we characterize the oriented trees achieving this lower bound.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 1; 67-79
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Signed Roman Edge k -Domination in Graphs
    Autorzy:
    Asgharsharghi, Leila
    Sheikholeslami, Seyed Mahmoud
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31342188.pdf
    Data publikacji:
    2017-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed Roman edge k -dominating function
    signed Roman edge k -domination number
    Opis:
    Let $ k \ge 1 $ be an integer, and $ G = (V, E) $ be a finite and simple graph. The closed neighborhood $ N_G [e]$ of an edge $e$ in a graph $G$ is the set consisting of $e$ and all edges having a common end-vertex with $e$. A signed Roman edge $k$-dominating function (SREkDF) on a graph $G$ is a function $ f : E \rightarrow {−1, 1, 2} $ satisfying the conditions that (i) for every edge $e$ of $G$, $ \Sigma_{ x \in N_G [e] } f(x) \ge k $ and (ii) every edge e for which $f(e) = −1$ is adjacent to at least one edge $ e^′ $ for which $ f(e^′) = 2 $. The minimum of the values $ \Sigma_{e \in E} f(e) $, taken over all signed Roman edge $k$-dominating functions $f$ of $G$ is called the signed Roman edge $k$-domination number of $G$, and is denoted by $ \gamma_{sRk}^' (G) $. In this paper we initiate the study of the signed Roman edge $k$-domination in graphs and present some (sharp) bounds for this parameter.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 1; 39-53
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Upper Bounds on the Signed Total (k, k)-Domatic Number of Graphs
    Autorzy:
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31339301.pdf
    Data publikacji:
    2015-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed total (k
    k)-domatic number
    signed total k-dominating function
    signed total k-domination number
    regular graphs
    Opis:
    Let $G$ be a graph with vertex set $V (G)$, and let $ f : V (G) \rightarrow {−1, 1}$ be a two-valued function. If $ k \geq 1$ is an integer and \( \sum_{ x \in N(v)} f(x) \geq k \) for each $ v \in V (G) $, where $N(v)$ is the neighborhood of $v$, then $f$ is a signed total $k$-dominating function on $G$. A set ${f_1, f_2, . . ., f_d}$ of distinct signed total k-dominating functions on $G$ with the property that \( \sum_{i=1}^d f_i(x) \leq k \) for each $ x \in V (G)$, is called a signed total ($k$, $k$)-dominating family (of functions) on $G$. The maximum number of functions in a signed total ($k$, $k$)-dominating family on $G$ is the signed total ($k$, $k$)-domatic number of $G$. In this article we mainly present upper bounds on the signed total ($k$, $k$)- domatic number, in particular for regular graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2015, 35, 4; 641-650
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Signed Total Roman k-Domatic Number Of A Graph
    Autorzy:
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31341581.pdf
    Data publikacji:
    2017-11-27
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed total Roman k-dominating function
    signed total Roman k-domination number
    signed total Roman k-domatic number
    Opis:
    Let $ k \ge 1 $ be an integer. A signed total Roman $k$-dominating function on a graph $G$ is a function $ f : V (G) \rightarrow {−1, 1, 2} $ such that $ \Sigma_{ u \in N(v) } f(u) \ge k $ for every $ v \in V (G) $, where $ N(v) $ is the neighborhood of $ v $, and every vertex $ u \in V (G) $ for which $ f(u) = −1 $ is adjacent to at least one vertex w for which $ f(w) = 2 $. A set $ { f_1, f_2, . . ., f_d} $ of distinct signed total Roman $k$-dominating functions on $G$ with the property that $ \Sigma_{i=1}^d f_i(v) \le k $ for each $ v \in V (G) $, is called a signed total Roman $k$-dominating family (of functions) on $G$. The maximum number of functions in a signed total Roman $k$-dominating family on $G$ is the signed total Roman $k$-domatic number of $G$, denoted by $ d_{stR}^k (G) $. In this paper we initiate the study of signed total Roman $k$-domatic numbers in graphs, and we present sharp bounds for $ d_{stR}^k (G) $. In particular, we derive some Nordhaus-Gaddum type inequalities. In addition, we determine the signed total Roman $k$-domatic number of some graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 4; 1027-1038
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

      Ta witryna wykorzystuje pliki cookies do przechowywania informacji na Twoim komputerze. Pliki cookies stosujemy w celu świadczenia usług na najwyższym poziomie, w tym w sposób dostosowany do indywidualnych potrzeb. Korzystanie z witryny bez zmiany ustawień dotyczących cookies oznacza, że będą one zamieszczane w Twoim komputerze. W każdym momencie możesz dokonać zmiany ustawień dotyczących cookies