Temat: dominating set - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: A Note on the Locating-Total Domination in Graphs
Autorzy:: Miller, Mirka
Rajan, R. Sundara
Jayagopal, R.
Rajasingh, Indra
Manuel, Paul
Tematy:: dominating set
total dominating set
locating-dominating set
locating-total dominating set
regular graphs; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31341658.pdf Link otwiera się w nowym oknie
Opis:: In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Connected odd dominating sets in graphs
Autorzy:: Caro, Yair
Klostermeyer, William
Yuster, Raphael
Tematy:: dominating set
odd dominating set; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/744351.pdf Link otwiera się w nowym oknie
Opis:: An odd dominating set of a simple, undirected graph G = (V,E) is a set of vertices D ⊆ V such that |N[v] ∩ D| ≡ 1 mod 2 for all vertices v ∈ V. It is known that every graph has an odd dominating set. In this paper we consider the concept of connected odd dominating sets. We prove that the problem of deciding if a graph has a connected odd dominating set is NP-complete. We also determine the existence or non-existence of such sets in several classes of graphs. Among other results, we prove there are only 15 grid graphs that have a connected odd dominating set.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Making a Dominating Set of a Graph Connected
Autorzy:: Li, Hengzhe
Wu, Baoyindureng
Yang, Weihua
Tematy:: independent set
dominating set
connected dominating set; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31342251.pdf Link otwiera się w nowym oknie
Opis:: Let $ G = (V,E) $ be a graph and $ S \subseteq V $. We say that $ S $ is a dominating set of $ G $, if each vertex in $ V \backlash S $ has a neighbor in $S$. Moreover, we say that $S$ is a connected (respectively, 2-edge connected or 2-connected) dominating set of $G$ if $ G[S] $ is connected (respectively, 2-edge connected or 2-connected). The domination (respectively, connected domination, or 2-edge connected domination, or 2-connected domination) number of $G$ is the cardinality of a minimum dominating (respectively, connected dominating, or 2-edge connected dominating, or 2-connected dominating) set of $G$, and is denoted $ \gamma (G) $ (respectively $ \gamma_1 (G) $, or $ \gamma_2^′ (G) $, or $ \gamma_2 (G) $). A well-known result of Duchet and Meyniel states that $ \gamma_1 (G) \le 3 \gamma (G) − 2 $ for any connected graph $G$. We show that if $ \gamma (G) \ge 2 $, then $ \gamma_2^′ (G) \ge 5 \gamma (G) − 4 $ when $G$ is a 2-edge connected graph and $ \gamma_2 (G) \le 11 \gamma (G) − 13 $ when $G$ is a 2-connected triangle-free graph.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Hereditary Equality of Domination and Exponential Domination in Subcubic Graphs
Autorzy:: Chen, Xue-Gang
Wang, Yu-Feng
Wu, Xiao-Fei
Tematy:: dominating set
exponential dominating set
subcubic graphs; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32324524.pdf Link otwiera się w nowym oknie
Opis:: Let γ(G) and γ_e(G) denote the domination number and exponential domination number of graph G, respectively. Henning et al., in [Hereditary equality of domination and exponential domination, Discuss. Math. Graph Theory 38 (2018) 275–285] gave a conjecture: There is a finite set ℱ of graphs such that a graph G satisfies (H) = γ_e(H) for every induced subgraph H of G if and only if G is ℱ-free. In this paper, we study the conjecture for subcubic graphs. We characterize the class ℱ by minimal forbidden induced subgraphs and prove that the conjecture holds for subcubic graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Independent transversal domination in graphs
Autorzy:: Hamid, Ismail
Tematy:: dominating set
independent set
independent transversal dominating set; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743635.pdf Link otwiera się w nowym oknie
Opis:: A set S ⊆ V of vertices in a graph G = (V, E) is called a dominating set if every vertex in V-S is adjacent to a vertex in S. A dominating set which intersects every maximum independent set in G is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by $γ_{it}(G)$. In this paper we begin an investigation of this parameter.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Odd and residue domination numbers of a graph
Autorzy:: Caro, Yair
Klostermeyer, William
Goldwasser, John
Tematy:: dominating set
odd dominating set
parity domination; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743442.pdf Link otwiera się w nowym oknie
Opis:: Let G = (V,E) be a simple, undirected graph. A set of vertices D is called an odd dominating set if |N[v] ∩ D| ≡ 1 (mod 2) for every vertex v ∈ V(G). The minimum cardinality of an odd dominating set is called the odd domination number of G, denoted by γ₁(G). In this paper, several algorithmic and structural results are presented on this parameter for grids, complements of powers of cycles, and other graph classes as well as for more general forms of "residue" domination.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: Eternal Domination: Criticality and Reachability
Autorzy:: Klostermeyer, William F.
MacGillivray, Gary
Tematy:: dominating set
eternal dominating set
critical graphs; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31342174.pdf Link otwiera się w nowym oknie
Opis:: We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached. The study of the stronger assertion that such a set can be reached after a single attack is defended leads to the study of graphs which are critical in the sense that deleting any vertex reduces the eternal domination number. Examples of these graphs and tight bounds on connectivity, edge-connectivity and diameter are given. It is also shown that there exist graphs in which deletion of any edge increases the eternal domination number, and graphs in which addition of any edge decreases the eternal domination number.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: On minimum intersections of certain secondary dominating sets in graphs
Autorzy:: Kosiorowska, Anna
Michalski, Adrian
Włoch, Iwona
Tematy:: dominating set
2-dominating set
(1, 2)-dominating set
proper (1, 2)-dominating set
domination number
(1,2)-intersection index; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/29519420.pdf Link otwiera się w nowym oknie
Opis:: In this paper we consider secondary dominating sets, also named as (1,k)-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the (1, 1)-dominating sets and proper (1, 2)-dominating sets. We introduce (1,2̅)-intersection index as the minimum possible cardinality of such intersection and determine its value for some classes of graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: Quasiperfect domination in triangular lattices
Autorzy:: Dejter, Italo
Tematy:: perfect dominating set
quasiperfect dominating set
triangular lattice; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743129.pdf Link otwiera się w nowym oknie
Opis:: A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G∖S is adjacent to only one vertex ($d_v$ ∈ {1,2} vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol {3,6} and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets S with induced components of the form $K_ν$, where ν ∈ {1,2,3} depends only on S.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Autorzy:: Rad, Nader Jafari
Rahbani, Hadi
Tematy:: locating-dominating set
differentiating-total dominating set
tree; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31342324.pdf Link otwiera się w nowym oknie
Opis:: A subset $S$ of vertices in a graph $G = (V,E)$ is a dominating set of $G$ if every vertex in $V − S$ has a neighbor in $S$, and is a total dominating set if every vertex in $V$ has a neighbor in $S$. A dominating set $S$ is a locating-dominating set of $G$ if every two vertices $ x, y \in V − S$ satisfy $N(x) \cap S \ne N(y) \cap S$. The locating-domination number $ \gamma_L (G) $ is the minimum cardinality of a locating-dominating set of $G$. A total dominating set $S$ is called a differentiating-total dominating set if for every pair of distinct vertices $u$ and $v$ of $G$, $ N[u] \cap S \ne N[v] \cap S $. The minimum cardinality of a differentiating-total dominating set of $G$ is the differentiating-total domination number of $G$, denoted by $ \gamma_t^D (G) $. We obtain new upper bounds for the locating-domination number, and the differentiating-total domination number in trees. Moreover, we characterize all trees achieving equality for the new bounds.
Dostawca treści:: Biblioteka Nauki

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