Temat: total - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Characterization of cubic graphs $G$ with $ir_t(G)=IR_t(G)=2$
Autorzy:: Eslahchi, Changiz
Haghi, Shahab
Jafari Rad, Nader
Tematy:: total domination
total irredundance
cubic; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/30148358.pdf Link otwiera się w nowym oknie
Opis:: A subset $S$ of vertices in a graph $G$ is called a total irredundant set if, for each vertex $v$ in $G$, $v$ or one of its neighbors has no neighbor in $S −{v}$. The total irredundance number, $ir(G)$, is the minimum cardinality of a maximal total irredundant set of $G$, while the upper total irredundance number, $IR(G)$, is the maximum cardinality of a such set. In this paper we characterize all cubic graphs $G$ with $ir_t(G) = IR_t(G) = 2$.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: General sharp upper bounds on the total coalition number
Autorzy:: Barát, János
Blázsik, Zoltán
Tematy:: total domination
total coalition partition
total coalition number
total coalition graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/59901678.pdf Link otwiera się w nowym oknie
Opis:: Let $G(V,E)$ be a finite, simple, isolate-free graph. Two disjoint sets $A,B\subset V$ form a total coalition in $G$, if none of them is a total dominating set, but their union $A\cup B$ is a total dominating set. A vertex partition $\Psi=\{C_1,C_2,...,C_k\}$ is a total coalition partition, if none of the partition classes is a total dominating set, meanwhile for every $i\in\{1,2,...,k\}$ there exists a distinct $j\in\{1,2,...,k\}$ such that $C_i$ and $C_j$ form a total coalition. The maximum cardinality of a total coalition partition of $G$ is the total coalition number of $G$ and denoted by $TC(G)$. We give a general sharp upper bound on the total coalition number as a function of the maximum degree. We further investigate this optimal case and study the total coalition graph. We show that every graph can be realised as a total coalition graph.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Total Domination Multisubdivision Number of a Graph
Autorzy:: Avella-Alaminos, Diana
Dettlaff, Magda
Lemańska, Magdalena
Zuazua, Rita
Tematy:: (total) domination
(total) domination subdivision number
(total) domination multisubdivision number
trees; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31339480.pdf Link otwiera się w nowym oknie
Opis:: The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_γt (G) of a graph G and we show that for any connected graph G of order at least two, msd_γt (G) ≤ 3. We show that for trees the total domination multisubdivision number is equal to the known total domination subdivision number. We also determine the total domination multisubdivision number for some classes of graphs and characterize trees T with msd_γt (T) = 1.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Total Protection of Lexicographic Product Graphs
Autorzy:: Martínez, Abel Cabrera
Rodríguez-Velázquez, Juan Alberto
Tematy:: total weak Roman domination
secure total domination
total domination
lexicographic product; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32304140.pdf Link otwiera się w nowym oknie
Opis:: Given a graph G with vertex set V (G), a function f : V (G) → {0, 1, 2} is said to be a total dominating function if Σ_u∈N(v) f(u) > 0 for every v ∈ V (G), where N(v) denotes the open neighbourhood of v. Let V_i = {x ∈ V (G) : f(x) = i}. A total dominating function f is a total weak Roman dominating function if for every vertex v ∈ V₀ there exists a vertex u ∈ N(v) ∩ (V₁ ∪ V₂) such that the function f′, defined by f′(v) = 1, f′(u) = f(u) − 1 and f′(x) = f(x) whenever x ∈ V (G) \ {u, v}, is a total dominating function as well. If f is a total weak Roman dominating function and V₂ = ∅, then we say that f is a secure total dominating function. The weight of a function f is defined to be ω(f) = Σ_v∈V (G) f(v). The total weak Roman domination number (secure total domination number) of a graph G is the minimum weight among all total weak Roman dominating functions (secure total dominating functions) on G. In this article, we show that these two parameters coincide for lexicographic product graphs. Furthermore, we obtain closed formulae and tight bounds for these parameters in terms of invariants of the factor graphs involved in the product.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Bounds On The Disjunctive Total Domination Number Of A Tree
Autorzy:: Henning, Michael A.
Naicker, Viroshan
Tematy:: total domination
disjunctive total domination
trees; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31341124.pdf Link otwiera się w nowym oknie
Opis:: Let $G$ be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, $ \gamma_t(G) $. A set $S$ of vertices in $G$ is a disjunctive total dominating set of $G$ if every vertex is adjacent to a vertex of $S$ or has at least two vertices in $S$ at distance 2 from it. The disjunctive total domination number, $ \gamma_t^d (G) $, is the minimum cardinality of such a set. We observe that $ \gamma_t^d (G) \ge \gamma_t (G) $. A leaf of $G$ is a vertex of degree 1, while a support vertex of $G$ is a vertex adjacent to a leaf. We show that if $T$ is a tree of order $n$ with $ \mathcal{l} $ leaves and $s$ support vertices, then $ 2(n−\mathcal{l}+3) // 5 \le \gamma_t^d (T) \le (n+s−1)//2 $ and we characterize the families of trees which attain these bounds. For every tree $T$, we show have $ \gamma_t(T) // \gamma_t^d (T) <2 $ and this bound is asymptotically tight.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: An upper bound on the total outer-independent domination number of a tree
Autorzy:: Krzywkowski, M.
Tematy:: total outer-independent domination
total domination
tree; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255991.pdf Link otwiera się w nowym oknie
Opis:: A total outer-independent dominating set of a graph G = (V (G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent. The total outer-independent domination number of a graph G, denoted by [formula], is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n ≥ 4, with l leaves and s support vertices we have [formula], and we characterize the trees attaining this upper bound.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: Total Domination in Generalized Prisms and a New Domination Invariant
Autorzy:: Tepeh, Aleksandra
Tematy:: domination
k -rainbow total domination
total domination; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32222717.pdf Link otwiera się w nowym oknie
Opis:: In this paper we complement recent studies on the total domination of prisms by considering generalized prisms, i.e., Cartesian products of an arbitrary graph and a complete graph. By introducing a new domination invariant on a graph G, called the k-rainbow total domination number and denoted by γ_krt(G), it is shown that the problem of finding the total domination number of a generalized prism G □ K_k is equivalent to an optimization problem of assigning subsets of {1, 2, . . ., k} to vertices of G. Various properties of the new domination invariant are presented, including, inter alia, that γ_krt(G) = n for a nontrivial graph G of order n as soon as k ≥ 2Δ(G). To prove the mentioned result as well as the closed formulas for the k-rainbow total domination number of paths and cycles for every k, a new weight-redistribution method is introduced, which serves as an efficient tool for establishing a lower bound for a domination invariant.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: The total {k}-domatic number of digraphs
Autorzy:: Sheikholeslami, Seyed
Volkmann, Lutz
Tematy:: digraph
total {k}-dominating function
total {k}-domination number
total {k}-domatic number; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743233.pdf Link otwiera się w nowym oknie
Opis:: For a positive integer k, a total {k}-dominating function of a digraph D is a function f from the vertex set V(D) to the set {0,1,2, ...,k} such that for any vertex v ∈ V(D), the condition $∑_{u ∈ N^{ -}(v)}f(u) ≥ k$ is fulfilled, where N¯(v) consists of all vertices of D from which arcs go into v. A set ${f₁,f₂, ...,f_d}$ of total {k}-dominating functions of D with the property that $∑_{i = 1}^d f_i(v) ≤ k$ for each v ∈ V(D), is called a total {k}-dominating family (of functions) on D. The maximum number of functions in a total {k}-dominating family on D is the total {k}-domatic number of D, denoted by $dₜ^{{k}}(D)$. Note that $dₜ^{{1}}(D)$ is the classic total domatic number $dₜ(D)$. In this paper we initiate the study of the total {k}-domatic number in digraphs, and we present some bounds for $dₜ^{{k}}(D)$. Some of our results are extensions of well-know properties of the total domatic number of digraphs and the total {k}-domatic number of graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: Bounds on the Locating-Total Domination Number in Trees
Autorzy:: Wang, Kun
Ning, Wenjie
Lu, Mei
Tematy:: tree
total dominating set
locating-total dominating set
locating-total domination number; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31867549.pdf Link otwiera się w nowym oknie
Opis:: Given a graph $G = (V, E)$ with no isolated vertex, a subset $S$ of $V$ is called a total dominating set of $G$ if every vertex in $V$ has a neighbor in $S$. A total dominating set $S$ is called a locating-total dominating set if for each pair of distinct vertices $u$ and $v$ in $V \ S, N(u) ∩ S ≠ N(v) ∩ S$. The minimum cardinality of a locating-total dominating set of $G$ is the locating-total domination number, denoted by $γ_t^L(G)$. We show that, for a tree $T$ of order $n ≥ 3$ and diameter $d$, $\frac{d+1}{2}≤γ_t^L(T)≤n−\frac{d−1}{2}$, and if $T$ has $l$ leaves, $s$ support vertices and $s_1$ strong support vertices, then $γ_t^L(T)≥max\Big\{\frac{n+l−s+1}{2}−\frac{s+s_1}{4},\frac{2(n+1)+3(l−s)−s_1}{5}\Big\}$. We also characterize the extremal trees achieving these bounds.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: Chapter 1 : Human body composition and muscle mass
Autorzy:: Duda, Krzysztof
Majerczak, Joanna
Heymsfield, Steven B.
Nieckarz, Zenon
Zoladz, Jerzy A.
Wydawca:: Academic Press
Opis:: Knowledge on body composition is important both in health and in disease, especially when considering chronic (i.e., growing, ageing, pregnancy) and interventional (nutrition, exercise, physical training) biological processes, as well as in predicting, preventing and managing such modern chronic diseases as sarcopenia, obesity, type 2 diabetes or metabolic syndrome. Therefore, in this chapter we present human body composition by taking advantage of widely accepted models, from the simplest 2-compartment model, which allows fat and fat-free body mass to be distinguished, up to a more complex, 6-compartment model, capable of distinguishing body fat, total body water, bone minerals, proteins, soft-tissue minerals, and glycogen. Moreover, in this chapter we provide equations that can be applied in laboratory and clinical practice to predict the main components of body composition, such as body water, skeletal muscles (SMs), body fat, and bone minerals. Special attention is given to the methods of evaluation of SM mass and its importance in health and disease.
Dostawca treści:: Repozytorium Uniwersytetu Jagiellońskiego

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