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Journal articles on the topic 'Domination number'

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Published: 4 June 2021

Last updated: 26 July 2025

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1

Esakkimuthu, A., and S. Mari Selvam. "Equitable Color Class Domination Number of Honeycomb Networks Graph and Inverse Equitable Color Class Domination Number of a Graph." Indian Journal Of Science And Technology 17, no. 36 (2024): 3800–3810. http://dx.doi.org/10.17485/ijst/v17i36.2458.

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Objectives: In this study, we find a new graph domination parameter named “Inverse Equitable Color Class Domination” and discuss the equitable color class domination number of honeycomb networks graph. Methods: Let be a connected graph. Assume a group containing colors. Let be an equitably colorable function. A dominating subset of is called an equitable color class dominating set if the number of dominating nodes in each color class is equal. The least possible cardinality of an equitable color class dominating set of is the equitable color class domination number itself. It is indicated by .

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Shanthi, P., S. Amutha, N. Anbazhagan, and G. Uma. "Fractional Star Domination Number of Graphs." Indian Journal Of Science And Technology 17, SPI1 (2024): 64–70. http://dx.doi.org/10.17485/ijst/v17sp1.111.

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Objectives: Consider a graph is the connected, undirected graph. This study creates a new parameter named the Fractional Star Domination Number (FRSDN), which is denoted by to calculate the minimum weight with the star of all vertices of and the function values of all edges. Methods: This study evaluates the of some standard graphs and bounds by generalizing the value that is provided by the function value of an edges. Findings: This study evaluated on some standard graphs, such as paths, cycles, and the rooted product of paths and cycles. Finally, we obtain some bounds on for some general gra

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3

Ilakkiya, D., and V. Mohana Selvi. "Odd and Co – Odd Sum Degree Domination in Graphs with Algorithm." Indian Journal Of Science And Technology 17, no. 32 (2024): 3368–76. http://dx.doi.org/10.17485/ijst/v17i32.1295.

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Objectives: The main aim of this study is to introduce two new domination parameters, namely odd and co-odd sum degree domination numbers, and to provide an algorithm for finding the odd sum degree dominating set of a graph. Methods: The odd and co-odd sum degree domination numbers of a graph G are introduced by verifying the following two conditions on dominating and co-dominating sets of G. (i) The sum of degree of vertices of the dominating and co-dominating sets are odd numbers. (ii) The cardinality of the above two sets are minimum. Further, obtained the degree sum values of the above two

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Mahadevan, G., P. Niveditha, and C. Sivagnanam. "Outer Triple Connected Corona Domination Number of Graphs." Indian Journal Of Science And Technology 17, SPI1 (2024): 136–43. http://dx.doi.org/10.17485/ijst/v17sp1.250.

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Background/ Objective: Given a graph G, a dominating set is said to be corona dominating set if every vertex such that or there exist a vertex if then . A corona dominating set is said to be an outer triple connected corona dominating set if any three vertices in lie on a path. The minimum cardinality taken over all the outer triple connected corona dominating sets of is called outer triple connected corona dominating number and it is denoted by . The study aims to find the outer triple connected corona domination number of some graphs. Method: To obtain outer triple connected corona dominatio

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Uma, G., S. Amutha, N. Anbazhagan, and P. Shanthi. "Fractional Domination Number of the Fractal Graphs." Indian Journal Of Science And Technology 17, SPI1 (2024): 34–39. http://dx.doi.org/10.17485/ijst/v17sp1.110.

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Background/Objectives: A fractal is a collection of clearly defined structures that are uneven or irregular and can be divided into smaller pieces. Each of these smaller pieces has a relationship to the overall structure at random ranges that are analogous or identical. Fractal graphs are a highly effective way to construct well-defined patterns. The fractional domination number in a graph refers to the weight of a minimum fractional dominating function. The study is to find the bounds of the fractional domination and their related parameters in the fractal graphs. Methods: The sharp bounds an

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Revathi, R., and P. Vidhya. "Tree Domination Number of Semi Total Point Graphs." Indian Journal Of Science And Technology 17, no. 30 (2024): 3109–15. http://dx.doi.org/10.17485/ijst/v17i30.1612.

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Objectives: The main aim of the research work is to study the concept of a tree domination number of semi-total point graphs. Method: A set D of a graph G = (V, E) is a dominating set, if every vertex in V- D is adjacent to at least one vertex in D. The domination number is the minimum cardinality of a dominating set D. A dominating set D is called a tree dominating set, if the induced subgraph is a tree. The minimum cardinality of a tree dominating set is called the tree-domination number of G and is denoted by . For any graph G = (V, E), the semi-total point graph T2(G) = H is the graph whos

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D, Ilakkiya, and Mohana Selvi V. "Odd and Co – Odd Sum Degree Domination in Graphs with Algorithm." Indian Journal of Science and Technology 17, no. 32 (2024): 3368–76. https://doi.org/10.17485/IJST/v17i32.1295.

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Abstract <strong>Objectives:</strong> The main aim of this study is to introduce two new domination parameters, namely odd and co-odd sum degree domination numbers, and to provide an algorithm for finding the odd sum degree dominating set of a graph. <strong>Methods:</strong> The odd and co-odd sum degree domination numbers of a graph G are introduced by verifying the following two conditions on dominating and co-dominating sets of G. (i) The sum of degree of vertices of the dominating and co-dominating sets are odd numbers. (ii) The cardinality of the above two sets are minimum

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Basavanagoud, B., and S. M. Hosamani. "Complete Cototal Domination Number of a Graph." Journal of Scientific Research 3, no. 3 (2011): 547–55. http://dx.doi.org/10.3329/jsr.v3i3.7744.

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Let be a graph. A set of a graph is called a total dominating set if the induced subgraph has no isolated vertices. The total domination number of G is the minimum cardinality of a total dominating set of G. A total dominating set D is said to be a complete cototal dominating set if the induced subgraph has no isolated vertices. The complete cototal domination number of G is the minimum cardinality of a complete cototal dominating set of G. In this paper, we initiate the study of complete cototal domination in graphs and present bounds and some exact values for . Also its relationship with oth

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Kaviya, S., G. Mahadevan, and C. Sivagnanam. "Generalizing TCCD-Number For Power Graph Of Some Graphs." Indian Journal Of Science And Technology 17, SPI1 (2024): 115–23. http://dx.doi.org/10.17485/ijst/v17sp1.243.

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Objective: Finding the triple connected certified domination number for the power graph of some peculiar graphs. Methods: A dominating set with the condition that every vertex in has either zero or at least two neighbors in and is triple connected is a called triple connected certified domination number of a graph. The minimum cardinality among all the triple connected certified dominating sets is called the triple connected certified domination number and is denoted by . The upper bound and lower bound of for the given graphs is found and then proved the upper bound and lower bound of were eq

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Praveenkumar, L., G. Mahadevan, and C. Sivagnanam. "Generalization of CD-Number for Power Graph of Some Special Types of Tree Graphs." Indian Journal Of Science And Technology 17, SPI1 (2024): 109–14. http://dx.doi.org/10.17485/ijst/v17sp1.223.

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Objectives: The main objective of the article is to finding the corona domination for the power graph of some special types of tree graph. Method: A dominating set of a graph is said to be a corona dominating set if every vertex in is either a pendant vertex or a support vertex. The minimum cardinality of a corona dominating set is called the corona domination number and is denoted by . Findings: In this article, we study the -number for the power of PVB-tree and where and identify their exact values. Novelty: The corona domination was one of the recently developed domination parameter, along

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A. Vijayalekshmi and S. Abisha. "An introduction of total dominator color class total dominating sets in graphs." Malaya Journal of Matematik 9, no. 01 (2021): 1225–28. http://dx.doi.org/10.26637/mjm0901/0212.

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Let $G$ be a finite, undirected and connected graph with minimum degree at least one. In this paper we define a new graph parameter called total dominator color class total domination number of $G$. A proper coloring $\mathcal{C}$ of $G$ is said to be a total dominator color class total dominating set of $G$ if each vertex properly dominates a color class in $\mathcal{C}$ and each color class in $\mathcal{C}$ is properly dominated by a vertex in $\mathrm{V}(\mathrm{G})$. A total dominator color class total dominating set $D$ of $G$ is a minimal total dominator color class total dominating set

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A, Mohamed Ismayil, and Priyadharshini R. "Inverse Detour Eccentric Domination in Graphs." Indian Journal of Science and Technology 17, SP1 (2024): 79–85. https://doi.org/10.5281/zenodo.13847564.

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Abstract <strong>Objective:</strong> To determine the inverse detour eccentric domination number, inverse independent detour eccentric domination number and inverse total detour eccentric domination number for well-kwon graphs. <strong>Methods:</strong> Method of proving by existential statement and proving by different cases are used to prove the theorem and by determining the proposed numbers using the least cardinality. <strong>Findings:</strong> Inverse detour domination number and other numbers are determined and the relation between the proposed number and other

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A, Esakkimuthu, and Mari Selvam S. "Equitable Color Class Domination Number of Honeycomb Networks Graph and Inverse Equitable Color Class Domination Number of a Graph." Indian Journal of Science and Technology 17, no. 36 (2024): 3800–3810. https://doi.org/10.17485/IJST/v17i36.2458.

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Abstract <strong>Objectives:</strong> In this study, we find a new graph domination parameter named “Inverse Equitable Color Class Domination” and discuss the equitable color class domination number of honeycomb networks graph. <strong>Methods:</strong> Let be a connected graph. Assume a group containing colors. Let be an equitably colorable function. A dominating subset of is called an equitable color class dominating set if the number of dominating nodes in each color class is equal. The least possible cardinality of an equitable color class dominating set of is th

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Priya, M. Santhosh, та A. Mydeen Bibi. "Enclave Domination Number of Semi Total Graphs 𝑇 𝟏(𝐺) and𝑇 𝟐(𝐺)". Indian Journal Of Science And Technology 18, № 9 (2025): 671–81. https://doi.org/10.17485/ijst/v18i9.3958.

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Objectives: This research seeks to explore the concept of enclave domination in semi total line graphs, semi total point graphs, and to establish the sharp bounds and key properties of the enclave domination number in these graphs. Methods: This investigation explores enclave domination in semi-total graphs by identifying dominating sets that meet the specific requirements of enclave domination. The process involves determining vertex subsets where each vertex outside the set is adjacent to at least one vertex within it, with particular attention to the unique structural characteristics of sem

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Chellali, Mustapha, and Nader Jafari Rad. "Trees with independent Roman domination number twice the independent domination number." Discrete Mathematics, Algorithms and Applications 07, no. 04 (2015): 1550048. http://dx.doi.org/10.1142/s1793830915500482.

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A Roman dominating function (RDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] for which [Formula: see text] is adjacent to at least one vertex [Formula: see text] for which [Formula: see text]. The weight of a RDF [Formula: see text] is the value [Formula: see text]. The Roman domination number, [Formula: see text], of [Formula: see text] is the minimum weight of a RDF on [Formula: see text]. An RDF [Formula: see text] is called an independent Roman dominating function (IRDF) if the set [Formula: see text] is a

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Bakhshesh, Davood. "Characterization of some classes of graphs with equal domination number and isolate domination number." Discrete Mathematics, Algorithms and Applications 12, no. 05 (2020): 2050065. http://dx.doi.org/10.1142/s1793830920500652.

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Let [Formula: see text] be a simple and undirected graph with vertex set [Formula: see text]. A set [Formula: see text] is called a dominating set of [Formula: see text], if every vertex in [Formula: see text] is adjacent to at least one vertex in [Formula: see text]. The minimum cardinality of a dominating set of [Formula: see text] is called the domination number of [Formula: see text], denoted by [Formula: see text]. A dominating set [Formula: see text] of [Formula: see text] is called isolate dominating, if the induced subgraph [Formula: see text] of [Formula: see text] contains at least o

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Shalini, V., and Indra Rajasingh. "Inverse Domination in X-Trees and Sibling Trees." European Journal of Pure and Applied Mathematics 17, no. 2 (2024): 1082–93. http://dx.doi.org/10.29020/nybg.ejpam.v17i2.5038.

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A set $D$ of vertices in a graph $G$ is a dominating set if every vertex not in $D$ is adjacent to at least one vertex in $D$. The minimum cardinality of a dominating set in $G$ is called the domination number and is denoted by $\gamma(G)$. Let $D$ be a minimum dominating set of $G$. If $V-D$ contains a dominating set say $D^{'}$ of $G$, then $D^{'}$ is called an inverse dominating set with respect to $D$. The inverse domination number $\gamma^{'}(G)$ is the cardinality of a minimum inverse dominating set of $G$. A dominating set $D$ is called a connected dominating set or an independent domin

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Yasir Alrikabi, Zainab, Ahmed A. Omran, Sarah Ali Abdulkareem та Tushar Aggarwal. "Co-regular captive domination number γcrg in graphs". Journal of Discrete Mathematical Sciences and Cryptography 28, № 2 (2025): 569–75. https://doi.org/10.47974/jdmsc-2259.

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This paper initiated the new domination number, which is named the co-regular captive, it is linked to two numbers of dominations they are captive domination number (CDN) and r-regular captive domination number. Many of the bounded, properties, and theorems of this domination are determined.

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., Kokilambal. "ANTIPODAL DOMINATION NUMBER OF GRAPHS." South East Asian J. of Mathematics and Mathematical Sciences 18, no. 03 (2022): 339–46. http://dx.doi.org/10.56827/seajmms.2022.1803.28.

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A dominating set S V is said to be an Antipodal Dominating Set(ADS) of a connected graph G if there exist vertices x, y S such that d(x, y) = diam(G). The minimum cardinality of an ADS is called the Antipodal Domination Number(ADN), and is denoted by γap(G). In this paper, we determined the antipodal domination number for various graph prod- ucts, bound for antipodal domination and characterize the graphs with γap(G) = 2.

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S, Kavitha, and Robinson C. S. "Private Edge Domination Number of a Graph." Journal of Scientific Research 5, no. 2 (2013): 283–94. http://dx.doi.org/10.3329/jsr.v5i2.12024.

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A set is said to be a private edge dominating set, if it is an edge dominating set, for every has at least one external private neighbor in . Let and denote the minimum and maximum cardinalities, respectively, of a private edge dominating sets in a graph . In this paper we characterize connected graph for which ? q/2 and the graph for some upper bounds. The private edge domination numbers of several classes of graphs are determined.Keywords: Edge domination; Perfect domination; Private domination; Edge irredundant sets.© 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All r

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Pan, Zhuo, Peng Pan, and Chongshan Tie. "On the Relation Between the Domination Number and Edge Domination Number of Trees and Claw-Free Cubic Graphs." Mathematics 13, no. 3 (2025): 534. https://doi.org/10.3390/math13030534.

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For a connected graph G=(V,E), the dominating set in graph G is a subset of vertices F⊂V such that every vertex of V−F is adjacent to at least one vertex of F. The minimum cardinality of a dominating set of G, denoted by γ(G), is the domination number of G. The edge dominating set in graph G is a subset of edges S⊂E such that every edge of E−S is adjacent to at least one edge of S. The minimum cardinality of an edge dominating set of G, denoted by γ′(G), is the edge domination number of G. In this paper, we characterize all trees and claw-free cubic graphs with equal domination and edge domina

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Agustiarini, Efni, and A. N. M. Salman. "The Non-Isolated Domination Number of a Graph." Jurnal Matematika, Statistika dan Komputasi 21, no. 3 (2025): 786–95. https://doi.org/10.20956/j.v21i3.43474.

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A subset S of the vertex set V (G) of a graph G is said to be a dominating set if every vertex not in S is adjacent to at least one vertex in S. In this research, we introduce a new domination parameter called the non-isolated domination number of a graph. A subset S of V of a nontrivial graph G is said to be a non-isolated dominating set if S is a dominating set and there are no zero-degree vertices in the subgraph induced by S. The minimum cardinality taken over all non-isolated dominating sets is called the non-isolated domination number and is denoted by γI. In this research, we obtained l

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Casinillo, Emily L., Leomarich F. Casinillo, Jorge S. Valenzona, and Divina L. Valenzona. "On Triangular Secure Domination Number." InPrime: Indonesian Journal of Pure and Applied Mathematics 2, no. 2 (2020): 105–10. http://dx.doi.org/10.15408/inprime.v2i2.15996.

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Let T_m=(V(T_m), E(T_m)) be a triangular grid graph of m ϵ N level. The order of graph T_m is called a triangular number. A subset T of V(T_m) is a dominating set of T_m if for all u_V(T_m)\T, there exists vϵT such that uv ϵ E(T_m), that is, N[T]=V(T_m). A dominating set T of V(T_m) is a secure dominating set of T_m if for each u ϵ V(T_m)\T, there exists v ϵ T such that uv ϵ E(T_m) and the set (T\{u})ꓴ{v} is a dominating set of T_m. The minimum cardinality of a secure dominating set of T_m, denoted by γ_s(T_m) is called a secure domination number of graph T_m. A secure dominating number γ_s(T_

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Meybodi, M. Alambardar, M. R. Hooshmandasl, P. Sharifani, and A. Shakiba. "Domination cover number of graphs." Discrete Mathematics, Algorithms and Applications 11, no. 02 (2019): 1950020. http://dx.doi.org/10.1142/s1793830919500204.

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A set [Formula: see text] for the graph [Formula: see text] is called a dominating set if any vertex [Formula: see text] has at least one neighbor in [Formula: see text]. Fomin et al. [Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications, ACM Transactions on Algorithms (TALG) 5(1) (2008) 9] gave an algorithm for enumerating all minimal dominating sets with [Formula: see text] vertices in [Formula: see text] time. It is known that the number of minimal dominating sets for interval graphs and trees on [Formula: see text] vertices is at most [Formula: se

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Suahas, P. Gade, and K. Vyavahare Dayanand. "Lict k-Domination in Graphs." Indian Journal of Science and Technology 17, no. 13 (2024): 1315–22. https://doi.org/10.17485/IJST/v17i13.3114.

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Abstract <strong>Objectives:</strong> In this study, we find lict -domination number of various types of graphs. <strong>Methods:</strong> Let be any graph, a set is said to be an -dominating set of lict graph if every vertex is dominated by at least vertices in , that is . The Lict -domination number is the minimum cardinality of -dominating set of .<strong> Findings:</strong> This study is centered on the lict -domination number of the graph and developed its relationship with other different domination parameters. <strong>Novelty:</strong> This study intro

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Dettlaff, Magda, Magdalena Lemańska, Mateusz Miotk, Jerzy Topp, Radosław Ziemann, and Paweł Żyliński. "Graphs with equal domination and certified domination numbers." Opuscula Mathematica 39, no. 6 (2019): 815–27. http://dx.doi.org/10.7494/opmath.2019.39.6.815.

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A set \(D\) of vertices of a graph \(G=(V_G,E_G)\) is a dominating set of \(G\) if every vertex in \(V_G-D\) is adjacent to at least one vertex in \(D\). The domination number (upper domination number, respectively) of \(G\), denoted by \(\gamma(G)\) (\(\Gamma(G)\), respectively), is the cardinality of a smallest (largest minimal, respectively) dominating set of \(G\). A subset \(D\subseteq V_G\) is called a certified dominating set of \(G\) if \(D\) is a dominating set of \(G\) and every vertex in \(D\) has either zero or at least two neighbors in \(V_G-D\). The cardinality of a smallest (lar

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G, Rajasekar, and G. Rajasekar. "Reserved Domination Number of Line Graph." Mapana Journal of Sciences 22, Special Issue (2023): 51–62. https://doi.org/10.12723/mjs.sp1.5.

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The reserved dominating set is special up gradation of domination set; where in some of the vertices in the vertex set have special privilege (reserved) to appear in the Dominating set irrespective of their adjacency due to the necessity of the user. The minimum cardinality of a reserved dominating set of G is called the reserved domination number of G and is denoted by R(k) -Y(G) where k is the number of reserved vertices. In this paper reserved domination number of (LPn), (LCn), L(Sn), L(Bm,n), L(Wn) and L(F l,n ) have been found.

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Vaidya, S. K., and P. D. Ajani. "Restrained Edge Domination Number of Some Path Related Graphs." Journal of Scientific Research 13, no. 1 (2021): 145–51. http://dx.doi.org/10.3329/jsr.v13i1.48520.

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For a graph G = (V,E), a set S ⊆ V(S ⊆ E) is a restrained dominating (restrained edge dominating) set if every vertex (edge) not in S is adjacent (incident) to a vertex (edge) in S and to a vertex (edge) in V - S(E-S). The minimum cardinality of a restrained dominating (restrained edge dominating) set of G is called restrained domination (restrained edge domination) number of G, denoted by γr (G) (γre(G). The restrained edge domination number of some standard graphs are already investigated while in this paper the restrained edge domination number like degree splitting, switching, square and m

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Vaidya, S. K., and P. D. Ajani. "Restrained Edge Domination Number of Some Path Related Graphs." Journal of Scientific Research 13, no. 1 (2021): 145–51. http://dx.doi.org/10.3329/jsr.v13i1.48520.

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For a graph G = (V,E), a set S ⊆ V(S ⊆ E) is a restrained dominating (restrained edge dominating) set if every vertex (edge) not in S is adjacent (incident) to a vertex (edge) in S and to a vertex (edge) in V - S(E-S). The minimum cardinality of a restrained dominating (restrained edge dominating) set of G is called restrained domination (restrained edge domination) number of G, denoted by γr (G) (γre(G). The restrained edge domination number of some standard graphs are already investigated while in this paper the restrained edge domination number like degree splitting, switching, square and m

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S.B. Anupama, Y. B. Maralabhavi, and Venkanagouda M. Goudar. "Cototal edge domination number of a graph." Malaya Journal of Matematik 4, no. 02 (2016): 325–37. http://dx.doi.org/10.26637/mjm402/017.

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A set $F$ of a graph $G(V, E)$ is an edge dominating set if every edge in $E-F$ is adjacent to some edge in $F$. An edge domination number $\gamma^{\prime}(G)$ of $G$ is the minimum cardinality of an edge dominating set. An edge dominating set $F$ is called a cototal edge dominating set if the induced subgraph $\langle E-F\rangle$ doesnot contain isolated edge. The minimum cardinality of the cototal edge dominating set in $G$ is its domination number and is denoted by $\gamma_{c o t}^{\prime}(G)$. We investigate several properties of cototal edge dominating sets and give some bounds on the cot

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V. Mary, Gleeta, and Priya C. N. Celine. "The hull domination number of a graph." i-manager’s Journal on Mathematics 13, no. 1 (2024): 38. http://dx.doi.org/10.26634/jmat.13.1.20570.

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For a connected graph G = (V, E), the hull number h(G) of a graph G is the minimum cardinality of a set of vertices whose convex hull contains all vertices of G. A hull set S in a connected graph G is called a minimal hull set of G if no proper subset of S is a hull set of G.A subset D of vertices in G is called a dominating set if every vertex not in D has at least one neighbor in D. A Hull dominating set M is both a Hull and a dominating set. The hull (domination, hull domination) number h(G),(γ(G),γh(G)) of G is the minimum cardinality among all hull (dominating, hull dominating) sets in G.

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P, Shanthi, Amutha S, Anbazhagan N, and Uma G. "Fractional Star Domination Number of Graphs." Indian Journal of Science and Technology 17, SP1 (2024): 64–70. https://doi.org/10.17485/IJST/v17sp1.111.

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Abstract <strong>Objectives</strong>: Consider a graph is the connected, undirected graph. This study creates a new parameter named the Fractional Star Domination Number (FRSDN), which is denoted by to calculate the minimum weight with the star of all vertices of and the function values of all edges. <strong>Methods:</strong> This study evaluates the of some standard graphs and bounds by generalizing the value that is provided by the function value of an edges. <strong>Findings:</strong> This study evaluated on some standard graphs, such as paths, cycles, and the rooted pro

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Almalki, Norah, and Pawaton Kaemawichanurat. "Domination and Independent Domination in Hexagonal Systems." Mathematics 10, no. 1 (2021): 67. http://dx.doi.org/10.3390/math10010067.

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A vertex subset D of G is a dominating set if every vertex in V(G)\D is adjacent to a vertex in D. A dominating set D is independent if G[D], the subgraph of G induced by D, contains no edge. The domination number γ(G) of a graph G is the minimum cardinality of a dominating set of G, and the independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. A classical work related to the relationship between γ(G) and i(G) of a graph G was established in 1978 by Allan and Laskar. They proved that every K1,3-free graph G satisfies γ(G)=i(H). Hexagonal syst

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G, Mahadevan, Niveditha P, and Sivagnanam C. "Outer Triple Connected Corona Domination Number of Graphs." Indian Journal of Science and Technology 17, SP1 (2024): 136–43. https://doi.org/10.17485/IJST/v17sp1.250.

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Abstract <strong>Background/ Objective:</strong> Given a graph G, a dominating set is said to be corona dominating set if every vertex such that or there exist a vertex if then . A corona dominating set is said to be an outer triple connected corona dominating set if any three vertices in lie on a path. The minimum cardinality taken over all the outer triple connected corona dominating sets of is called outer triple connected corona dominating number and it is denoted by . The study aims to find the outer triple connected corona domination number of some graphs. <strong>Method:</stro

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Kuriachan, Geethu, and A. Parthiban. "On Graph Entropy Measures Based on the Number of Dominating and Power Dominating Sets." Malaysian Journal of Mathematical Sciences 19, no. 1 (2025): 269–87. https://doi.org/10.47836/mjms.19.1.14.

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This article examines graph entropy measures that depend on the number of dominating and power-dominating sets. To quantify the structural complexity of a graph structure, one uses graph entropies. It is easy to compute these properties for smaller networks, and if reliable approximations are developed, similar metrics can also be used for larger graphs. Using various graph invariants, many graph entropy measures have already been established and computed. So, in this work, a new graph entropy measure, namely, power domination entropy, using the power domination polynomial, is introduced. The

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G, Uma, Amutha S, Anbazhagan N, and Shanthi P. "Fractional Domination Number of the Fractal Graphs." Indian Journal of Science and Technology 17, SP1 (2024): 34–39. https://doi.org/10.17485/IJST/v17sp1.110.

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Abstract <strong>Background/Objectives:</strong> A fractal is a collection of clearly defined structures that are uneven or irregular and can be divided into smaller pieces. Each of these smaller pieces has a relationship to the overall structure at random ranges that are analogous or identical. Fractal graphs are a highly effective way to construct well-defined patterns. The fractional domination number in a graph refers to the weight of a minimum fractional dominating function. The study is to find the bounds of the fractional domination and their related parameters in the fractal graph

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R, Revathi, and Vidhya P. "Tree Domination Number of Semi Total Point Graphs." Indian Journal of Science and Technology 17, no. 30 (2024): 3109–15. https://doi.org/10.17485/IJST/v17i30.1612.

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Abstract <strong>Objectives:</strong> The main aim of the research work is to study the concept of a tree domination number of semi-total point graphs. <strong>Method:</strong> A set D of a graph G = (V, E) is a dominating set, if every vertex in V- D is adjacent to at least one vertex in D. The domination number is the minimum cardinality of a dominating set D. A dominating set D is called a tree dominating set, if the induced subgraph is a tree. The minimum cardinality of a tree dominating set is called the tree-domination number of G and is denoted by . For any graph G = (V,

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Et. al., S. Muthammai,. "Nonsplit Neighbourhood Tree Domination Number In Connected Graphs." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 9 (2021): 3237–44. http://dx.doi.org/10.17762/turcomat.v12i9.5444.

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: Let G = (V, E) be a connected graph. A subset D of V is called a dominating set of G if N[D] = V. The minimum cardinality of a dominating set of G is called the domination number of G and is denoted by g(G). A dominating set D of a graph G is called a tree dominating set (tr - set) if the induced subgraph áDñ is a tree. The tree domination number γtr(G) of G is the minimum cardinality of a tree dominating set. A tree dominating set D of a graph G is called a neighbourhood tree dominating set (ntr - set) if the induced subgraph áN(D)ñ is a tree. The neighbourhood tree domination number γntr(G

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KLOBUČAR BARIŠIĆ, ANA, and ANTOANETA KLOBUČAR. "Double Total Domination Number on Some Chemical Nanotubes." Kragujevac Journal of Mathematics 50, no. 3 (2024): 415–23. http://dx.doi.org/10.46793/kgjmat2603.415b.

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Suppose G is a graph with the vertex set V (G). A set D ⊆ V (G) is a total k-dominating set if every vertex v ∈ V (G) has at least k neighbours in D. The total k-domination number γkt(G) is the size of the smallest total k-dominating set. When k = 2 the total 2-dominating set is referred to as a double total dominating set. In this work we compute the exact values for double total domination number on H-phenylenic nanotubes HPH(m,n), m,n ≥ 2 and H-naphtalenic nanotubes HN(m,n), n = 2k, m,n ≥ 2. As all vertices have a degree 2 or 3, there is no total k-domination for k ≥ 3 for H-phenylenic and

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Dettlaff, Magda, Saeed Kosary, Magdalena Lemańska, and Seyed Sheikholeslami. "Weakly convex domination subdivision number of a graph." Filomat 30, no. 8 (2016): 2101–10. http://dx.doi.org/10.2298/fil1608101d.

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A set X is weakly convex in G if for any two vertices a,b ? X there exists an ab-geodesic such that all of its vertices belong to X. A set X ? V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number ?wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd?wcon (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the weakly convex domination number. In this paper we initiate the stu

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Atay, Betül. "Domination and bondage number for double vertex graphs of some graphs." Filomat 38, no. 31 (2024): 11007–16. https://doi.org/10.2298/fil2431007a.

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If a network modeled by a graph, then there are various graph theoretical parameters used to express the vulnerability and stability of communication networks. One of them is the concept of bondage number based on domination. The dominating set of a graph is a vertex set in that every vertex which is not in the dominating set is adjacent to at least one vertex of the dominating set. The domination number is the minimal cardinality among all dominating sets. The bondage number of any graph is the minimal cardinality among all sets of edges whose removal from the graph results in a graph with do

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Stalin, D., and John Johnson. "Edge geodetic fault tolerant domination number of a graph." Proyecciones (Antofagasta) 43, no. 5 (2024): 1055–73. http://dx.doi.org/10.22199/issn.0717-6279-6387.

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For a connected graph G = (V, E), a set F⊆V is said to be an edge geodetic fault tolerant dominating set of G if F is both edge geodetic set and fault tolerant dominating set of G. The minimum cardinality of an edge geodetic fault tolerant dominating set of G is called the edge geodetic fault tolerant domination number of G and is denoted by γgeft(G). The edge geodetic fault tolerant domination number of certain classes of graphs are determined. It is shown that for each pair of integers 3 ≤a < b, there exists a connected graph G such that γ(G) = a, γge (G)= b and γgeft(G) = a + b-1, where

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Muthupandiyan, S., and A. Mohamed Ismayil. "Upper g- Eccentric Domination in Fuzzy Graphs." Indian Journal Of Science And Technology 17, SPI1 (2024): 45–51. http://dx.doi.org/10.17485/ijst/v17sp1.142.

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Objectives: To introduce a contemporary aspect notorious as upper g-eccentric point set, upper g-eccentric number, upper g-eccentric dominating set, upper g-eccentric domination number in fuzzy graphs and related concepts. Methods: Strong arc in fuzzy graphs concepts are used to find upper g-eccentric number and upper g-eccentric domination number. Findings: The new idea upper g-eccentric domination in fuzzy graphs will leads to numerous application such as cell phone tower formation in remote areas. Novelty: Using the concepts g-distance, geodesics and strong arc in fuzzy graphs, the upper g-

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Cabrera Martínez, Abel, Luis P. Montejano, and Juan A. Rodríguez-Velázquez. "On the Secure Total Domination Number of Graphs." Symmetry 11, no. 9 (2019): 1165. http://dx.doi.org/10.3390/sym11091165.

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A total dominating set D of a graph G is said to be a secure total dominating set if for every vertex u ∈ V ( G ) \ D , there exists a vertex v ∈ D , which is adjacent to u, such that ( D \ { v } ) ∪ { u } is a total dominating set as well. The secure total domination number of G is the minimum cardinality among all secure total dominating sets of G. In this article, we obtain new relationships between the secure total domination number and other graph parameters: namely the independence number, the matching number and other domination parameters. Some of our results are tight bounds that impr

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Omran, Ahmed Abed Ali, and Essam El-Seidy. "Independence and inverse domination in complete z-ary tree and Jahangir graphs." Boletim da Sociedade Paranaense de Matemática 41 (December 26, 2022): 1–9. http://dx.doi.org/10.5269/bspm.53123.

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This article includes different properties of the independence and domination (total domination, independent domination, co-independent domination) number of the complete z-ray root and Jahangir graphs. Also, the inverse domination number of these graphs of variant dominating sets (total dominating, independent dominating, co-independent dominating) is determined.

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Jamil, Ferdinand P., and Hearty Nuenay Maglanque. "Cost Effective Domination in the Join, Corona and Composition of Graphs." European Journal of Pure and Applied Mathematics 12, no. 3 (2019): 978–98. http://dx.doi.org/10.29020/nybg.ejpam.v12i3.3443.

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Let $G$ be a connected graph. A cost effective dominating set in a graph $G$ is any set $S$ of vertices in $G$ satisfying the condition that each vertex in $S$ is adjacent to at least as many vertices outside $S$ as inside $S$ and every vertex outside $S$ is adjacent to at least one vertex in $S$. The minimum cardinality of a cost effective dominating set is the cost effective domination number of $G$. The maximum cardinality of a cost effective dominating set is the upper cost effective domination number of $G$. A cost effective dominating set is said to be minimal if it does not contain a pr

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Stalin, D., and J. John. "THE GEODETIC FAULT TOLERANT DOMINATION NUMBER OF A GRAPH." South East Asian J. of Mathematics and Mathematical Sciences 19, no. 01 (2023): 399–412. http://dx.doi.org/10.56827/seajmms.2023.1901.31.

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For a connected graph G = (V,E), a set F ⊆ V of vertices in G is called dominating set if every vertex not in F has at least one neighbor in F. A dominating set F ⊆ V is called fault tolerant dominating set if F − {v} is dominating set for every v ∈ F. A fault tolerant dominating set is said to be geodetic fault tolerant dominating set if I[F] = V . The minimum cardinality of a geodetic fault tolerant dominating set is called geodetic fault tolerant domination number and is denoted by γgft(G). The minimum geodetic fault tolerant dominating set is denoted by γgft-set. The geodetic fault toleran

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Senthilkumar, B., Yanamandram B. Venkatakrishnan, and H. Naresh Kumar. "DOMINATION AND EDGE DOMINATION IN TREES." Ural Mathematical Journal 6, no. 1 (2020): 147. http://dx.doi.org/10.15826/umj.2020.1.012.

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Let \(G=(V,E)\) be a simple graph. A set \(S\subseteq V\) is a dominating set if every vertex in \(V \setminus S\) is adjacent to a vertex in \(S\). The domination number of a graph \(G\), denoted by \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\). A set \(D \subseteq E\) is an edge dominating set if every edge in \(E\setminus D\) is adjacent to an edge in \(D\). The edge domination number of a graph \(G\), denoted by \(\gamma'(G)\) is the minimum cardinality of an edge dominating set of \(G\). We characterize trees with domination number equal to twice edge domination nu

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Humaizah, R., Dafik, A. I. Kristiana, I. H. Agustin, and E. Y. Kurniawati. "On the resolving strong domination number of some wheel related graphs." Journal of Physics: Conference Series 2157, no. 1 (2022): 012015. http://dx.doi.org/10.1088/1742-6596/2157/1/012015.

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Abstract This study aims to analyse the resolving strong dominating set. This concept combinations of two notions, they are metric dimension and strong domination set. By a resolving strong domination set, we mean a set D s ⊂ V(G) which satisfies the definition of strong dominating set as well as resolving set. The resolving strong domination number of graph G, denoted by γrst (G), is the minimum cardinality of resolving strong dominating set of G. In this paper, we determine the resolving strong domination number of some wheel related graphs, namely helm graph Hn , gear graph Gn , and flower

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A. Mohamed Ismayil and S. Ismail Mohideen. "Mixed domination in an M-strong fuzzy graph." Malaya Journal of Matematik 3, no. 02 (2015): 153–60. http://dx.doi.org/10.26637/mjm302/003.

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In this paper, mixed dominating set, mixed domination number, mixed strong domination number and mixed weak domination number of an M-strong fuzzy graph $G=(\sigma, \mu)$ are defined. Also these numbers are determined for various standard fuzzy graphs. The relationship between these numbers and other well known numbers are derived.

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