Relevant bibliographies by topics / Minimum equitable domination set

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Academic literature on the topic 'Minimum equitable domination set'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Minimum equitable domination set"

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ANITHA, A., S. ARUMUGAM, and MUSTAPHA CHELLALI. "EQUITABLE DOMINATION IN GRAPHS." Discrete Mathematics, Algorithms and Applications 03, no. 03 (2011): 311–21. http://dx.doi.org/10.1142/s1793830911001231.

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Let D be a dominating set of a graph G = (V, E). For v ∈ D, let n1(v) = |N(v) ∩ (V - D)| and for w ∈ V - D, let n2(w) = |N(w) ∩ D|. Then D is called an equitable dominating set of type 1 if |n1(v1) - n1(v2)| ≤ 1 for all v1, v2 ∈ D and is called an equitable dominating set of type 2 if |n2(w1) - n2(w2)| ≤ 1 for all w1, w2 ∈ V - D. The minimum cardinality of an equitable dominating set of G of type 1 (type 2) is called the 1-equitable (2-equitable) domination number of G and is denoted by γ eq1 (G)(γ eq2 (G)). If D is an equitable dominating set of type 1 and type 2, then D is called an equitabl
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Caay, Mark, Rodolfo Maza, Rafael Duarte, Sergii R. Lana, Bril Soriano, and April Janer. "Equitable isolate domination in graphs." Gulf Journal of Mathematics 19, no. 1 (2025): 337–46. https://doi.org/10.56947/gjom.v19i1.2603.

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A subset S ⊆ V(G) is said to an equitable isolate dominating set of a graph G if it is both equitable dominating set of G and isolate dominating set of G. The minimum cardinality of an equitable isolate dominating set is called equitable isolate domination number of G and is denoted by γe0 (G). An equitable isolate dominating set S of G is called γe0 -set of G. In this paper, the authors give characterizations of equitable isolate dominating set of some graphs and graphs obtained from the join and corona of two graphs. Furthermore, the equitable isolate domination numbers of these graphs is de
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Sumathi, P., and G. Alarmelumangai. "Locating Equitable Domination and Independence Subdivision Numbers of Graphs." Bulletin of Mathematical Sciences and Applications 9 (August 2014): 27–32. http://dx.doi.org/10.18052/www.scipress.com/bmsa.9.27.

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Let G = (V,E) be a simple, undirected, finite nontrivial graph. A non empty set DV of vertices in a graph G is a dominating set if every vertex in V-D is adjacent to some vertex in D. The domination number (G) is the minimum cardinality of a dominating set of G. A dominating set D is a locating equitable dominating set of G if for any two vertices u,wєV-D, N(u)∩D ≠ N(w)∩D, |N(u)∩D| ≠ |N(w)∩D|. The locating equitable domination number of G is the minimum cardinality of a locating equitable dominating set of G. The locating equitable domination subdivision number of G is the minimum number of ed
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Rana, Sohel, and Sk Md Abu Nayeem. "A linear time algorithm for minimum equitable dominating set in trees." Proyecciones (Antofagasta) 40, no. 4 (2021): 805–14. http://dx.doi.org/10.22199/issn.0717-6279-4552.

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Let G = (V, E) be a graph. A subset De of V is said to be an equitable dominating set if for every v ∈ V \ De there exists u ∈ De such that uv ∈ E and |deg(u) − deg(v)| ≤ 1, where, deg(u) and deg(v) denote the degree of the vertices u and v respectively. An equitable dominating set with minimum cardinality is called the minimum equitable dominating set and its cardinality is called the equitable domination number and it is denoted by γe. The problem of finding minimum equitable dominating set in general graphs is NP-complete. In this paper, we give a linear time algorithm to determine minimum
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Caay, Mark, and Andrew Hernandez. "Perfect Equitable Isolate Dominations in Graphs." European Journal of Pure and Applied Mathematics 17, no. 2 (2024): 969–78. http://dx.doi.org/10.29020/nybg.ejpam.v17i2.4963.

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A subset $S \subseteq V(G)$ is said to be a perfect equitable isolate dominating set of a graph $G$ if it is both perfect equitable dominating set of $G$ and isolate dominating set of $G$. The minimum cardinality of a perfect equitable isolate dominating set is called perfect equitable isolate domination number of $G$ and is denoted by $\gamma_{pe0}(G)$. A perfect equitable isolate dominating set $S$ of $G$ is called $\gamma_{pe0}$-set of $G$. In this paper, the authors give characterizations of a perfect equitable isolate dominating set of some graphs and graphs obtained from the join and cor
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M.S.Mahesh. "Some More Results On Neighborhood Connected Two Out Degree Equitable Domination Number Of Graphs." Advances in Nonlinear Variational Inequalities 28, no. 6s (2025): 522–28. https://doi.org/10.52783/anvi.v28.4337.

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For any graph G, the out degree of a vertex v with respect to D is denoted by and it is defined by). A sub set D of V(G) is said to be two out degree equitable dominating set if D is dominating set and for any two vertices such that The minimum number of vertices in two out degree equitable dominating set is called two out degree equitable domination number and it is denoted by Based on the above concept of out degree we introduce a new domination parameter called neighborhood connected two out degree equitable domination number and study this domination number for some standard graphs In this
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M.S.Mahesh. "Some More Results on Neighborhood Connected Two Out Degree Equitable Domination Number of Graphs." Advances in Nonlinear Variational Inequalities 28, no. 5s (2025): 438–45. https://doi.org/10.52783/anvi.v28.3914.

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For any graph G, the out degree of a vertex v with respect to D is denoted by and it is defined by). A sub set D of V(G) is said to be two out degree equitable dominating set if D is dominating set and for any two vertices such that The minimum number of vertices in two out degree equitable dominating set is called two out degree equitable domination number and it is denoted by Based on the above concept of out degree we introduce a new domination parameter called neighborhood connected two out degree equitable domination number and study this domination number for some standard graphs In this
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Vaidya, S. K., and N. J. Kothari. "Some Results on Equi Independent Equitable Dominating Sets in Graph." Journal of Scientific Research 7, no. 3 (2015): 77–85. http://dx.doi.org/10.3329/jsr.v7i3.23412.

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A subset D of V(G) is called an equitable dominating set if for every ? ? V(G) - D, there exists a vertex u ? D such that u? ? E(G) and | deg(u) – deg(?) | ? 1. A subset D of V(G) is called an equitable independent set if for any D of V(G), ? ? Ne(u) for all ? ? D - {u}where, Ne(u) = {? ? V(G)/? ? N(u), | deg(u) – deg(?) | ? 1}. An equitable dominating set D is said to be an equi independent equitable dominating set if it is also an equitable independent set. The minimum cardinality of an equi independent equitable dominating set is called equi independent equitable domination number which is
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Ameenal Bibi, K., та P. Rajakumari. "Neighborhood Connected Two -Outdegree Equitable Domination of the ϑ-Obrazom Graphs of P_n,G_n and H_n". International Journal of Engineering & Technology 7, № 4.10 (2018): 399. http://dx.doi.org/10.14419/ijet.v7i4.10.21025.

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Let G=(V,E) be a connected graph. A two-outdegree equitable dominating set D of a graph G is called the neighborhood connected two-outdegree equitable dominating set (nc2oe-set) if the induced sub graph <N(D)> is connected. The minimum cardinality of the minimal neighborhood connected two-outdegree equitable dominating set is called neighborhood connected two-outdegree equitable domination number of G and is denoted by . In this paper, we initiated the a study of this parameter and obtained for the -obrazom graphs of and . Also, we investigated the two-outdegree equitable domination numb
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T. R., Thasneem, and Manju K. Menon. "Outdegree equitable domination number of certain graph operators." Proyecciones (Antofagasta) 43, no. 5 (2024): 1037–53. http://dx.doi.org/10.22199/issn.0717-6279-6275.

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For a vertex u in the dominating set D of a graph G, the number of edges from u to V-D is called the outdegree of u with respect to D, d°D, G(u). A dominating set D is called the outdegree equitable dominating set if the absolute value of the differences of outdegrees of any two vertices in D is at most one. The minimum cardinality of an outdegree equitable dominating set of G is called the outdegree equitable domination number of G, γoe(G). In this paper, we study the outdegree equitable domination number of certain graph operators such as complement, double graph, mycielskian and subdivision
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Dissertations / Theses on the topic "Minimum equitable domination set"

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Lane, Stephen M. "Trees with Unique Minimum Locating-Dominating Sets." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2196.

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A set S of vertices in a graph G = (V, E) is a locating-dominating set if S is a dominating set of G, and every pair of distinct vertices {u, v} in V - S is located with respect to S, that is, if the set of neighbors of u that are in S is not equal to the set of neighbors of v that are in S. We give a construction of trees that have unique minimum locating-dominating sets.
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Book chapters on the topic "Minimum equitable domination set"

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Sampathkumar, E., and L. Pushpalatha. "Domination Theory in Graphs." In Handbook of Research on Advanced Applications of Graph Theory in Modern Society. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-5225-9380-5.ch001.

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The study of domination in graphs originated around 1850 with the problems of placing minimum number of queens or other chess pieces on an n x n chess board so as to cover/dominate every square. The rules of chess specify that in one move a queen can advance any number of squares horizontally, vertically, or diagonally as long as there are no other chess pieces in its way. In 1850 enthusiasts who studied the problem came to the correct conclusion that all the squares in an 8 x 8 chessboard can be dominated by five queens and five is the minimum such number. With very few exceptions (Rooks, Bis
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Chang Shun-Chieh, Liu Jia-Jie, and Wang Yue-Li. "The Weighted Independent Domination Problem in Series-Parallel Graphs." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2015. https://doi.org/10.3233/978-1-61499-484-8-77.

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A set S of vertices in a graph G=(V,E) is an independent dominating set of G if no two vertices in S are adjacent and every vertex not in S is adjacent to a vertex in S. Suppose every vertex v∈V and every edge e∈E are associated with a cost which is a real number, denoted by c(v) and c(e), respectively. The weighted independent domination problem is to find an independent dominating set D such that its total cost c(D)=Σx∈Dc(x)+Σx∉Dmin {c(x,y), for y&is
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Wooster, Henry. "Faith at the Ramparts: The Philippine Catholic Church and the 1986 Revolution." In Religion, The Missing Dimension of Statecraft. Oxford University PressNew York, NY, 1994. http://dx.doi.org/10.1093/oso/9780195087345.003.0008.

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Abstract Three centuries of Spanish domination of the Philippines were followed by American rule in the first half of the twentieth century, which set the stage for an era of close ties with the United States. Throughout the Cold War, two U.S. military bases there served as key assets and critical links to Asia. But the Philippines was unable to match the economic dynamism of its regional neighbors. The authoritarian rule of Ferdinand Marcos, who came to power in 1965, failed to achieve equitable economic growth and political stability. Population growth, poverty, and the lack of land reform,
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"Water Struggles in a Colonial City." In Waiting for the Cool Moon. Duke University Press, 2023. http://dx.doi.org/10.1215/9781478027829-008.

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Chapter 7 focuses on the refusals that were a regular response to imperialist domination in Okinawa. It engages Dionne Brand’s The Blue Clerk in order to read colonial ledgers as repositories of contestation rather than faithful assimilation, and argues that accepting opacity in the archives is the minimum starting point of a nonextractive historical practice. It tells the story of a struggle over water that erupted along the western coast of Okinawa island in the early 1930s, in and around the city of Naha. Despite previous narrations of what is referred to as the Ginowan water struggle as a
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Tweeddale, Andrew, and Keren Tweeddale. "The Arbitral Tribunal and Jurisdiction." In Arbitration of Commercial Disputes. Oxford University PressOxford, 2005. http://dx.doi.org/10.1093/oso/9780199265404.003.0005.

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Abstract The services that the arbitral tribunal provide have been stated as being ‘principally and habitually those of settling a dispute between two or more parties, even though this is done on an equitable basis’.1 The relationship between the parties and the arbitral tribunal is founded out of a contract and it is from this contract that the arbitral tribunal derives its jurisdiction. As stated in Ashville Investments v Elmer Contractors:2 ‘A non-statutory arbitrator derives his jurisdiction from the agreement of the parties at whose instance he is appointed. He has such jurisdiction as th
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Reports on the topic "Minimum equitable domination set"

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Ocampo-Gaviria, José Antonio, Roberto Steiner Sampedro, Mauricio Villamizar Villegas, et al. Report of the Board of Directors to the Congress of Colombia - March 2023. Banco de la República de Colombia, 2023. http://dx.doi.org/10.32468/inf-jun-dir-con-rep-eng.03-2023.

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Banco de la República is celebrating its 100th anniversary in 2023. This is a very significant anniversary and one that provides an opportunity to highlight the contribution the Bank has made to the country’s development. Its track record as guarantor of monetary stability has established it as the one independent state institution that generates the greatest confidence among Colombians due to its transparency, management capabilities, and effective compliance with the central banking and cultural responsibilities entrusted to it by the Constitution and the Law. On a date as important as this,
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SDG 4.1.1 Minimum Proficiency Levels. Definition and blueprint for assessment. Australian Council for Educational Research, 2025. https://doi.org/10.37517/978-1-74286-782-3.

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Sustainable Development Goal (SDG) 4 aims to ensure that, by 2030, “all girls and boys complete free, equitable and quality primary and secondary education leading to relevant and effective learning outcomes.” The primary indicator 4.1.1 concerns the proficiency of girls and boys in two learning areas (reading and mathematics) at three stages of education: at the end of lower primary, at the end of primary, and at the end of lower secondary. Large-scale learning assessments are essential tools to capture data on learning outcomes and to provide system-level evidence on education quality and eq
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