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Journal articles on the topic 'Subdivision of Star graph'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

K.Sunitha. "Radial Radio Pell Mean Labeling of Subdivision of Graphs." Advances in Nonlinear Variational Inequalities 28, no. 2 (2024): 267–73. http://dx.doi.org/10.52783/anvi.v28.1969.

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A one-one mapping ϕ : V (G) → N for a connected graph G is defined as follows: d(x,y)+⌈(ϕ(x)+2ϕ(y))/2⌉≥1+r(G), where radius is denoted by r(G). Any vertex in G has a radial radio pell mean number of ϕ which is the maximum number and is represented by rrpmn(ϕ). Here, we look at the labeling of various graphs using the radial radio pell mean of subdivisions such as subdivision of star graph S(K_(1,n)) , subdivision of path graph S(Pn) , subdivision of friendship graph S(Fn), subdivision of wheel graph S(Wn), subdivision of quadrilateral book graph S(QB(4,3)), subdivision of closed helm graph S(C

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Sasikala, C. Muthulakshmi @., and A. Akil Nivetha. "Exploring Mean Cordial Labeling Possible Combination Position of Vertices in Graphs: A Computational Approach." Indian Journal Of Science And Technology 17, no. 39 (2024): 4111–18. http://dx.doi.org/10.17485/ijst/v17i39.2915.

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Objectives: We have developed the Python module of mean cordial labeling for the different types of graphs, like Path, Cycle, and Subdivision of Star graphs. We aim to identify the number of combination positions of vertices that satisfy the mean cordial labeling rules. We have found mathematical equations that describe the labeling behavior in these graphs. Methods: In this paper, a Python program was developed to find the mean cordial labeling of the Path, Cycle, and Subdivision of the Star graph. We have obtained the number of combination positions of vertex obeying the mean cordial labelin

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3

C, Muthulakshmi @Sasikala, and Akil Nivetha A. "Exploring Mean Cordial Labeling Possible Combination Position of Vertices in Graphs: A Computational Approach." Indian Journal of Science and Technology 17, no. 39 (2024): 4111–18. https://doi.org/10.17485/IJST/v17i39.2915.

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Abstract <strong>Objectives:</strong> We have developed the Python module of mean cordial labeling for the different types of graphs, like Path, Cycle, and Subdivision of Star graphs. We aim to identify the number of combination positions of vertices that satisfy the mean cordial labeling rules. We have found mathematical equations that describe the labeling behavior in these graphs. <strong>Methods:</strong> In this paper, a Python program was developed to find the mean cordial labeling of the Path, Cycle, and Subdivision of the Star graph. We have obtained the number of combin

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4

P, Sumathi, and Chandravadana N. "Lucas Antimagic Labeling of some Star Related Graphs." Indian Journal of Science and Technology 15, no. 46 (2022): 2542–47. https://doi.org/10.17485/IJST/v15i46.1862.

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Abstract <strong>Objective:</strong> To identify a new family of Lucas antimagic graph.<strong> Methods:</strong> A (p;q) graph G is said to be a Lucas antimagic graph if there exists a bijection f : E(G) ! fL1;L2; Lqg such that the induced injective function f : V(G) ! f1;2; : : :åLqg given by f (u) = åe2E(u) f (e) are all distinct (where E(u) is the set of edges incident to u). <strong>Findings:</strong> In this paper the Lucas Antimagic Labeling of Subdivision of star, Shadow graph of star, Splitting graph of star, Subdivision of Bistar, Shadow graph of

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R, Charishma, and Nageswari P. "Cordial Labeling of Subdivision of Central Edge of Bistar Graph and Spider Graph." Indian Journal of Science and Technology 16, no. 35 (2023): 2889–93. https://doi.org/10.17485/IJST/v16i35.679.

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Abstract <strong>Objectives:</strong> To analyse cordial labelling of subdivision of central edge of bistar graph and Spider graph. <strong>Methods:</strong> Cordial labeling is defined as a function g : V (q ) ! f0;1g in which each edge ab is assigned the label jg(a)􀀀g(b)j with the conditions vg(0)􀀀vg(1) 1 and eg(0)􀀀eg(1) 1 1 where v g ( 0 ) and v g ( 1 ) signify the number of vertices with 0’s and 1’s, similarly eg (0) and eg (1) signify the number of edges with 0’s and 1’s. <strong>Findings:</strong> In this paper, it is proved that subdivisi

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Amrullah, S. Azmi, H. Soeprianto, M. Turmuzi, and Y. S. Anwar. "The partition dimension of subdivision graph on the star." Journal of Physics: Conference Series 1280 (November 2019): 022037. http://dx.doi.org/10.1088/1742-6596/1280/2/022037.

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7

Awais, M. "Antimagic Behavior of S G p n and its Subdivision." Journal of Corrosion and Materials 48, no. 1 (2024): 65–68. http://dx.doi.org/10.61336/jcm2023-7.

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A finite simple graph G with a subgraph H is called a super (b, d)-H-antimagic: if G has an edge covering by subgraphs H1,H2, . . . ,Ht with each Hi∼= H, i = 1, 2, . . . , t, a total labeling α such that wtαH, constitutes an arithmetic progression and α(V (G)) consists of the smallest possible integers. In this manuscript, we investigated the existence of super (b, 1)- star-antimagic labeling of Sun graphs S G p n

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Falcón, Raúl M., M. Venkatachalam, and S. Julie Margaret. "Determining the b-chromatic number of subdivision-vertex neighbourhood coronas." Analele Universitatii "Ovidius" Constanta - Seria Matematica 32, no. 2 (2024): 53–84. https://doi.org/10.2478/auom-2024-0019.

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Abstract Let G and H be two graphs, each one of them being a path, a cycle or a star. In this paper, we determine the b-chromatic number of every subdivision-vertex neighbourhood corona G ⊡ H or G ⊡ K n, where K n is the complete graph of order n. It is also established for those graphs K n ⊡ G having m-degree not greater than n + 2. All the proofs are accompanied by illustrative examples.

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9

Kanwal, Salma, Ayesha Riasat, Mariam Imtiaz, Zurdat Iftikhar, Sana Javed, and Rehana Ashraf. "Bounds of Strong EMT Strength for certain Subdivision of Star and Bistar." Open Mathematics 16, no. 1 (2018): 1313–25. http://dx.doi.org/10.1515/math-2018-0111.

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AbstractA super edge-magic total (SEMT) labeling of a graph ℘(V, E) is a one-one map ϒ from V(℘)∪E(℘) onto {1, 2,…,|V (℘)∪E(℘) |} such that ∃ a constant “a” satisfying ϒ(υ) + ϒ(υν) + ϒ(ν) = a, for each edge υν ∈E(℘), moreover all vertices must receive the smallest labels. The super edge-magic total (SEMT) strength, sm(℘), of a graph ℘ is the minimum of all magic constants a(ϒ), where the minimum runs over all the SEMT labelings of ℘. This minimum is defined only if the graph has at least one such SEMT labeling. Furthermore, the super edge-magic total (SEMT) deficiency for a graph ℘, signified

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10

Qiang, Xiaoli, Saeed Kosari, Zehui Shao, Seyed Mahmoud Sheikholeslami, Mustapha Chellali, and Hossein Karami. "A Note on the Paired-Domination Subdivision Number of Trees." Mathematics 9, no. 2 (2021): 181. http://dx.doi.org/10.3390/math9020181.

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For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n≥4 different from a healthy spider (subdivided star), then sdγpr(T)≤min{γpr(T)2+1,n2}, improving the (n−1)-upper bound that was recently proven.

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11

Castro, Jair, Ludwin A. Basilio, Gerardo Reyna, and Omar Rosario. "The differential on operator $ {{\mathcal{S}}({\Gamma})} $." Mathematical Biosciences and Engineering 20, no. 7 (2023): 11568–84. http://dx.doi.org/10.3934/mbe.2023513.

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<abstract><p>Consider a simple graph $ \Gamma = (V(\Gamma), E(\Gamma)) $ with $ n $ vertices and $ m $ edges. Let $ P $ be a subset of $ V(\Gamma) $ and $ B(P) $ the set of neighbors of $ P $ in $ V(\Gamma)\backslash P $. In the study of graphs, the concept of <italic>differential</italic> refers to a measure of how much the number of edges leaving a set of vertices exceeds the size of that set. Specifically, given a subset $ P $ of vertices, the differential of $ P $, denoted by $ \partial(P) $, is defined as $ |B(P)|-|P| $. The <italic>differential</italic&gt

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12

Hausawi, Yasser M., Zaid Alzaid, Olayan Alharbi, Badr Almutairi, and Basma Mohamed. "COMPUTING THE SECURE CONNECTED DOMINANT METRIC DIMENSION PROBLEM OF CLASSES OF GRAPHS." Advances and Applications in Discrete Mathematics 42, no. 3 (2025): 219–33. https://doi.org/10.17654/0974165825015.

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This paper investigates the NP-hard problem of finding the lowest secure connected domination metric dimension of graphs. If each vertex in can be uniquely recognized by its vector of distances to the vertices in Scddim, then every vertex set Scddim of a connected graph resolves . If the subgraph induced by Scddim is a nontrivial connected subgraph of , then the resolving set Scddim of is connected. That resolving set is dominating if each vertex in that is not an element of Scddim is a neighbor of some vertices in Scddim. If there is a in such that is a dominating set for any in , then the do

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13

Ekstein, Jan, Přemysl Holub, Tomáš Kaiser, Liming Xiong, and Shenggui Zhang. "Star subdivisions and connected even factors in the square of a graph." Discrete Mathematics 312, no. 17 (2012): 2574–78. http://dx.doi.org/10.1016/j.disc.2011.09.004.

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Belay, Melaku Berhe, Chunxiang Wang, Abdul Jalil M. Khalaf, Hamid Hosseini, and Mohammad Reza Farahani. "Topological indices of the subdivision graph and the line graph of subdivision graph of the wheel graph." Journal of Discrete Mathematical Sciences and Cryptography 24, no. 2 (2021): 589–601. http://dx.doi.org/10.1080/09720529.2021.1892317.

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15

Sugiarty, Vetty, Amrullah Amrullah, and Nurul Hikmah. "Metric Dimension of the Pinwheel Subdivision Graph K_1+mK_3." Sigma&Mu: Journal of Mathematics, Statistics and Data Science 3, no. 1 (2025): 32–40. https://doi.org/10.56566/sigmamu.v3i1.251.

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Metric dimension is an important concept in graph theory that is widely used in various fields, including navigation, network localization, and network design. The concept of metric dimension is the concept of determining the least marker vertex so that each vertex in the graph is distinguished from each other. The purpose of this research is to determine the metric dimension of the pinwheel subdivision graph ????1+????????3. The type of research used is pure research. By using graph structure and vertex distance analysis, this paper shows the value of the metric dimension of the subdivision g

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16

Nagarajan, S., and M. Durga. "Computing Y-index of Different Corona Products of Graphs." Asian Research Journal of Mathematics 19, no. 10 (2023): 67–74. http://dx.doi.org/10.9734/arjom/2023/v19i10729.

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The Y-index of a graph is defined by the sum of four of degrees of the vertices of a graph. Among the all topological indices the Zagreb indices have been used more considerably than any other topological indices in chemical literature. The concept of Corona Product is a recent inclusion to mathematical vocabulary. One of the most significant graph operations is the corona product of several generic and specific graphs, which is one of the most well-known graph products. In this study, we derive some explicit formulations of several corona product types, including subdivision-vertex corona, su

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17

Ahmad, Zaheer, Muhammad K. Jamil, Mohammad R. Farahani, Sudev Naduvath, and Hafiz Muhammad Afzal Siddiqui. "VERTEX WEIGHTED WIENER POLYNOMIALS OF THE SUBDIVISION GRAPH AND THE LINE GRAPH OF SUBDIVISION GRAPH OF THE WHEEL GRAPH." Advances and Applications in Discrete Mathematics 20, no. 2 (2019): 305–20. http://dx.doi.org/10.17654/dm020020305.

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18

Keerthi, G. Mirajkar* Bhagyashri R. Doddamani Priyanka Y. B. "THE REFORMULATED FIRST ZAGREB INDEX OF THE LINE GRAPHS OF THE SUBDIVISION GRAPH FOR CLASS OF GRAPHS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, no. 10 (2016): 144–49. https://doi.org/10.5281/zenodo.159334.

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The reformulated first Zagreb index is the edge version of first Zagreb index of chemical graph theory. The aim of this paper is to obtain an expression for the reformulated first Zagreb index of the some class of graphs such as Tadpole graph, Wheel graph, Ladder graph. Further we also obtain the reformulated first Zagreb index of the line graph, subdivision graph and line graph of subdivision graph for class of graphs.

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19

Hogben, Leslie, and Naomi Shaked-Monderer. "SPN Graphs." Electronic Journal of Linear Algebra 35 (February 1, 2019): 376–86. http://dx.doi.org/10.13001/1081-3810.3747.

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A simple graph G is an SPN graph if every copositive matrix having graph G is the sum of a positive semidefinite and nonnegative matrix. SPN graphs were introduced in [N. Shaked-Monderer. SPN graphs: When copositive = SPN. Linear Algebra Appl., 509:82{113, 2016.], where it was conjectured that the complete subdivision graph of K4 is an SPN graph. This conjecture is disproved, which in conjunction with results in the Shaked-Monderer paper show that a subdivision of K_4 is a SPN graph if and only if at most one edge is subdivided. It is conjectured that a graph is an SPN graph if and only if it

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20

Asif, Fatima. "Leap Zagreb and leap hyper-Zagreb indices of Jahangir and Jahangir derived graphs." Engineering and Applied Science Letters 3, no. 2 (2020): 1–8. https://doi.org/10.30538/psrp-easl2020.0036.

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Topological indices are numerical parameters of a graph which characterize its topology. The second degree of a vertex in a graph is equal to the number of its second neighbors. In this paper, we will compute leap Zagreb indices and leap hyper-Zagreb indices of Jahangir graph and its line graph based on the 2-distance degree of the vertices. Moreover we will compute the same indices for the subdivision graph and the line graph of the subdivision of Jahangir graph.

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21

Saravanakumar, Seenivasan, and K. Nagarajan. "Distant Divisor Graph of Subdivision of a Graph." International Journal of Mathematics and Soft Computing 4, no. 1 (2014): 51. http://dx.doi.org/10.26708/ijmsc.2014.1.4.06.

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22

Thumbakara, Rajesh K., Bobin George, and Jinta Jose. "Subdivision Graph, Power and Line Graph of a Soft Graph." Communications in Mathematics and Applications 13, no. 1 (2022): 75–85. http://dx.doi.org/10.26713/cma.v13i1.1669.

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23

Kousar, Imrana, Saima Nazeer, Abid Mahboob, Sana Shahid, and Yu-Pei Lv. "Numerous graph energies of regular subdivision graph and complete graph." AIMS Mathematics 6, no. 8 (2021): 8466–76. http://dx.doi.org/10.3934/math.2021491.

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Gayathri, M., and R. Rajkumar. "Adjacency and Laplacian spectra of variants of neighborhood corona of graphs constrained by vertex subsets." Discrete Mathematics, Algorithms and Applications 11, no. 06 (2019): 1950073. http://dx.doi.org/10.1142/s1793830919500733.

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In this paper, we define some variants of corona of graphs namely, subdivision (respectively, [Formula: see text]-graph, [Formula: see text]-graph, total) neighborhood corona, [Formula: see text]-graph (respectively, [Formula: see text]-graph, total) semi-edge neighborhood corona, [Formula: see text]-graph (respectively, total) semi-vertex neighborhood corona of graphs constrained by vertex subsets. These corona operations generalize some existing corona operations such as subdivision ([Formula: see text]-graph, [Formula: see text]-graph, total) double neighborhood corona, subdivision vertex (

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Lu, Pengli, Ke Gao, and Yumo Wu. "Signless Laplacian spectrum of a class of generalized corona and its application." Discrete Mathematics, Algorithms and Applications 10, no. 05 (2018): 1850060. http://dx.doi.org/10.1142/s179383091850060x.

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Let [Formula: see text] be a graph with [Formula: see text] edges, [Formula: see text] the subdivision graph of [Formula: see text] with [Formula: see text] the set of inserted vertices of [Formula: see text]. The generalized subdivision-edge corona graph [Formula: see text] of [Formula: see text] and [Formula: see text] is the graph obtained from [Formula: see text] and [Formula: see text] by joining the [Formula: see text]th vertex of [Formula: see text] to every vertex of [Formula: see text]. In this paper, we determine the [Formula: see text]-polynomial of the graph [Formula: see text]. Al

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Chen, Guojun, and Rongji Wang. "Triangular Mesh Surface Subdivision Based on Graph Neural Network." Applied Sciences 14, no. 23 (2024): 11378. https://doi.org/10.3390/app142311378.

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Mesh subdivision is a common mesh-processing algorithm used to improve model accuracy and surface smoothness. Its classical scheme adopts a fixed linear vertex update strategy and is implemented iteratively, which often results in excessive mesh smoothness. In recent years, a nonlinear subdivision method that uses neural network methods, called neural subdivision (NS), has been proposed. However, as a new scheme, its application scope and the effect of its algorithm need to be improved. To solve the above problems, a graph neural network method based on neural subdivision was used to realize m

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Scaria, Deena C., and G. Indulal. "The distance Laplacian and distance signless Laplacian spectrum of the subdivision-vertex join and subdivision-edge join of two regular graphs." Discrete Mathematics, Algorithms and Applications 11, no. 05 (2019): 1950053. http://dx.doi.org/10.1142/s1793830919500538.

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Let [Formula: see text] be a connected graph with a distance matrix [Formula: see text]. Let [Formula: see text] and [Formula: see text] be, respectively, the distance Laplacian matrix and the distance signless Laplacian matrix of graph [Formula: see text], where [Formula: see text] denotes the diagonal matrix of the vertex transmissions in [Formula: see text]. The eigenvalues of [Formula: see text] and [Formula: see text] constitute the distance Laplacian spectrum and distance signless Laplacian spectrum, respectively. The subdivision graph [Formula: see text] of a graph [Formula: see text] i

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Manjunatha, B. J., B. R. Rakshith, K. N. Prakasha, and N. V. Sayinath Udupa. "Distance Spectra of Some Double Join Operations of Graphs." International Journal of Mathematics and Mathematical Sciences 2024 (May 27, 2024): 1–8. http://dx.doi.org/10.1155/2024/2017748.

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In literature, several types of join operations of two graphs based on subdivision graph, Q-graph, R-graph, and total graph have been introduced, and their spectral properties have been studied. In this paper, we introduce a new double join operation based on H1,H2-merged subdivision graph. We compute the spectrum of a special block matrix and then use it to describe the distance spectra of some double join operations of graphs. At last, we give several families of distance equienergetic graphs of diameter 3.

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Deen, Mohamed R. Zeen El, and Ghada M. Elmahdy. "Different types of odd harmonious labeling of super subdivision of various graphs." Journal of Discrete Mathematical Sciences and Cryptography 27, no. 8 (2024): 2433–67. https://doi.org/10.47974/jdmsc-1945.

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If the vertices of a graph Γ(α, β), with α = |V(Γ)| and β = |E(Γ)|, can be labelled with unequal integers within the set [0, 2β – 1], so that the edges labels generated by the sum of the labels of the end vertices modulo 2β are distinct odd numbers from the set [1, 2β – 1]. Then, we regard the graph Γ(V, E) to be a semi-odd harmonic graph. An odd harmonious graph satisfies the additional condition that modular asthmatic is not done. A strong odd harmonious graph is defined as an odd harmonious graph whose vertices can be labelled with unequal integers from the set [0, β]. In this study, we int

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Bokhary, Syed Ahtsham Ul Haq, Khola Wahid, Usman Ali, Shreefa O. Hilali, Mohammed Alhagyan, and Ameni Gargouri. "Resolvability in Subdivision Graph of Circulant Graphs." Symmetry 15, no. 4 (2023): 867. http://dx.doi.org/10.3390/sym15040867.

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Circulant networks are a very important and widely studied class of graphs due to their interesting and diverse applications in networking, facility location problems, and their symmetric properties. The structure of the graph ensures that it is symmetric about any line that cuts the graph into two equal parts. Due to this symmetric behavior, the resolvability of these graph becomes interning. Subdividing an edge means inserting a new vertex on the edge that divides it into two edges. The subdivision graph G is a graph formed by a series of edge subdivisions. In a graph, a resolving set is a s

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Wei-Kuo, Chiang, and Chen Rong-Jaye. "The (n, k)-star graph: A generalized star graph." Information Processing Letters 56, no. 5 (1995): 259–64. http://dx.doi.org/10.1016/0020-0190(95)00162-1.

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Chen, Haiyan, and Fuji Zhang. "Spectral Dynamics of Graph Sequences Generated by Subdivision and Triangle Extension." Electronic Journal of Linear Algebra 32 (February 6, 2017): 454–63. http://dx.doi.org/10.13001/1081-3810.3583.

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For a graph G and a unary graph operation X, there is a graph sequence \G_k generated by G_0=G and G_{k+1}=X(G_k). Let Sp({G_k}) denote the set of normalized Laplacian eigenvalues of G_k. The set of limit points of \bigcup_{k=0}^\infty Sp(G_k)$, $\liminf_{k\rightarrow\infty}Sp(G_k) and $\limsup_{k\rightarrow \infty}Sp(G_k)$ are considered in this paper for graph sequences generated by two operations: subdivision and triangle extension. It is obtained that the spectral dynamic of graph sequence generated by subdivision is determined by a quadratic function, which is closely related to the the w

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G. Navamani. "Effects of Subdivision on Fair Domination in Cyclic Structures." Advances in Nonlinear Variational Inequalities 28, no. 4s (2025): 184–95. https://doi.org/10.52783/anvi.v28.3236.

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A fair dominating set (FDS) is a dominating set of a graph , such that all vertices in are dominated by the same number of vertices of . The fair domination number (FDN) is the minimum cardinality of a fair dominating set of , denoted by The domination subdivision number (FDSN) , represents the smallest number of edges in that needs to be subdivided (with each edge being subdivided at most once) to increase the domination number of the graph. The fair domination subdivision number, (or ) is the minimum number of edge subdivisions needed to be applied to the graph to increase (or decrease) the

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M., I. Moussa, and Badr E.M. "LADDER AND SUBDIVISION OF LADDER GRAPHS WITH PENDANT EDGES ARE ODD GRACEFUL." International Journal on Applications of Graph Theory in Wireless Ad hoc Networks and Sensor Networks(GRAPH-HOC) 8, no. 1 (2019): 1–8. https://doi.org/10.5281/zenodo.3351927.

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The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph Ln with m-pendant Ln  mk1 is odd graceful. We also show that the subdivision of ladder graph Ln with m-pendant S(Ln)  mk1 is odd graceful. Finally, we prove that all the subdivision of triangular snakes ( k   snake ) with pendant edges 1 ( ) k S snake mk    are odd graceful.

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Jebitha, M. K. Angel. "Domination Uniform Subdivision Number of Graph." International Journal of Mathematics Trends and Technology 27, no. 1 (2015): 1–5. http://dx.doi.org/10.14445/22315373/ijmtt-v27p501.

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Jemimal Chrislight, R., and Y. Therese Sunitha Mary. "The nonsplit domination in subdivision graph." Proyecciones (Antofagasta) 39, no. 5 (2020): 1113–20. http://dx.doi.org/10.22199/issn.0717-6279-2020-05-0068.

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Wei, Jianxin, Syed Ahtsham Ul Haq Bokhary, Ghulam Abbas, and Muhammad Imran. "Resolvability in Subdivision of Circulant Networks Cn1,k." Discrete Dynamics in Nature and Society 2020 (September 14, 2020): 1–11. http://dx.doi.org/10.1155/2020/4197678.

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Circulant networks form a very important and widely explored class of graphs due to their interesting and wide-range applications in networking, facility location problems, and their symmetric properties. A resolving set is a subset of vertices of a connected graph such that each vertex of the graph is determined uniquely by its distances to that set. A resolving set of the graph that has the minimum cardinality is called the basis of the graph, and the number of elements in the basis is called the metric dimension of the graph. In this paper, the metric dimension is computed for the graph Gn1

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Kaladevi, V., R. Murugesan, and K. Pattabiraman. "First reformulated Zagreb indices of some classes of graphs." Carpathian Mathematical Publications 9, no. 2 (2018): 134–44. http://dx.doi.org/10.15330/cmp.9.2.134-144.

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A topological index of a graph is a parameter related to the graph; it does not depend on labeling or pictorial representation of the graph. Graph operations plays a vital role to analyze the structure and properties of a large graph which is derived from the smaller graphs. The Zagreb indices are the important topological indices found to have the applications in Quantitative Structure Property Relationship(QSPR) and Quantitative Structure Activity Relationship(QSAR) studies as well. There are various study of different versions of Zagreb indices. One of the most important Zagreb indices is t

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Babikir, Ammar, Magda Dettlaff, Michael A. Henning, and Magdalena Lemańska. "Independent Domination Subdivision in Graphs." Graphs and Combinatorics 37, no. 3 (2021): 691–709. http://dx.doi.org/10.1007/s00373-020-02269-3.

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AbstractA set S of vertices in a graph G is a dominating set if every vertex not in S is ad jacent to a vertex in S. If, in addition, S is an independent set, then S is an independent dominating set. The independent domination number i(G) of G is the minimum cardinality of an independent dominating set in G. The independent domination subdivision number $$ \hbox {sd}_{\mathrm{i}}(G)$$ sd i ( 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 independent domination number. We show that for every connected graph G o

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Borah, Manash Protim, Karam Ratan Singh, and Shariefuddin Pirzada. "On the spectra of quasi join of graphs and families of integral graphs." Acta Universitatis Sapientiae, Mathematica 16, no. 1 (2025): 69–74. https://doi.org/10.47745/ausm-2024-0004.

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The subdivision graph S(G) of a graph G is formed by adding a new vertex into every edge of G. The quasi-corona subdivision-vertex join of two graphs G and G′ is a graph derived from S(G) and G′ by choosing a copy of S(G) and n1 copies of G′ and then connecting those vertices of S(G) which were in G to all the vertices of G′ . The quasicorona subdivision-edge join of two graphs G and G′ is a graph derived from S(G) and G′ by choosing a copy of S(G) and n1 copies of G′ and then connecting those vertices of S(G) which were not in G to all the vertices of G′. The adjacency, Laplacian and signless

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G. Navamani. "Optimizing Subdivisions on Fair Domination in Petersen Graph Structures." Advances in Nonlinear Variational Inequalities 28, no. 3s (2024): 20–29. https://doi.org/10.52783/anvi.v28.2845.

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A fair dominating set (FDS) J is a dominating set of a graph H, such that all vertices in V \J are dominated by the same number of vertices of J. The fair domination number (FDN) is the minimum cardinality of a fair dominating set of H, denoted by γ_fd (H). The domination subdivision number (FDSN) 〖Sd〗_γ (H), represents the smallest number of edges in H that needs to be subdivided (with each edge being subdivided at most once) to increase the domination number of the graph. The fair domination subdivision number, 〖Sd〗_(γ_fd)^+ (H) (or 〖Sd〗_(γ_fd)^- (H)) is the minimum number of edge subdivisio

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Hameed, Shehla, Muhammad Kamran Jamil, Muhammad Waheed, Muhammad Azeem, and Senesie Swaray. "Two Complex Graph Operations and their Exact Formulations on Topological Properties." Complexity 2022 (June 7, 2022): 1–15. http://dx.doi.org/10.1155/2022/6927111.

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Graph operations are utilized for developing complicated graph structures from basic graphs, and these basic graphs can help to understand the properties of complex networks. While on the other side, the topological descriptor is known as a numeric value that is associated with the graph of a network. It has enormous practical applications in chemistry and other fields of science. This particular work in this draft is the extended work and investigated the first, second, first multiplicative, first reformulated Zagreb indices, and the forgotten index of subdivision double corona and subdivisio

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Rajkumar, R., and M. Gayathri. "Spectra of (H1,H2)-merged subdivision graph of a graph." Indagationes Mathematicae 30, no. 6 (2019): 1061–76. http://dx.doi.org/10.1016/j.indag.2019.08.001.

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Al-Rumaima, Mahmoud, Abdu Alameri, Mohammed Al-Sharafi, et al. "Computation of wiener polynomial and index of line subdivision friendship and line subdivision bifriendship graphs using matlab program." Proyecciones (Antofagasta) 43, no. 1 (2024): 163–87. http://dx.doi.org/10.22199/issn.0717-6279-5584.

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A topological index is a branch of chemical graph theory that is vital to analyzing the physio-chemical characteristics of chemical compound structures divided into a degree-based molecular structure such as Zagreb indices, a distance-based molecular structure such as Wiener index, and a mixed such as Gutman index. In this paper, some definitions, results, and examples of Wiener polynomial and index for subdivision graph of friendship, bifriendship graphs, line subdivision graph of friendship, and bifriendship graphs were introduced. Moreover, we used the MATLAB program to calculate the Wiener

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Ahmad, Mukhtar, Saddam Hussain, Ulfat Parveen, Iqra Zahid, Muhammad Sultan, and Ather Qayyum. "On Degree-Based Topological Indices of Petersen Subdivision Graph." European Journal of Mathematical Analysis 3 (June 5, 2023): 20. http://dx.doi.org/10.28924/ada/ma.3.20.

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In this paper, we adequately describe the generalised petersen graph, expanding to the categories of graphs. We created a petersen graph, which is cyclic and has vertices that are arranged in the centre and nine gons plus one vertex, leading to the factorization of regular graphs. Petersen graph is still shown in graph theory literature, nevertheless.

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Farid, Faiz, Muhammad Javaid, and Ebenezer Bonyah. "Computing Connection Distance Index of Derived Graphs." Mathematical Problems in Engineering 2022 (July 18, 2022): 1–15. http://dx.doi.org/10.1155/2022/1439177.

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Distance based topological indices (TIs) play a vital role in the study of various structural and chemical aspects for the molecular graphs. The first distance-based TI is used to find the boiling point of paraffin. The connection distance (CD) index is a latest developed TI that is defined as the sum of all the products of distances between pair of vertices with the sum of their respective connection numbers . In this paper, we computed CD indices of the different derived graphs (subdivision graph S G , vertex-semitotal graph R G , edge-semitotal graph Q G and total graph T G obtained from th

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CHIANG, WEI-KUO, and RONG-JAYE CHEN. "TOPOLOGICAL PROPERTIES OF THE (n,k)-STAR GRAPH." International Journal of Foundations of Computer Science 09, no. 02 (1998): 235–48. http://dx.doi.org/10.1142/s0129054198000167.

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The star graph, though an attractive alternative to the hypercube, has a major drawback in that the number of nodes for an n-star graph must be n!, and thus considerably limits the choice of the number of nodes in the graph. In order to alleviate this drawback, the arrangement graph was recently proposed as a generalization of the star graph topology. The arrangement graph provides more flexibility than the star graph in choosing the number of nodes, but the degree of the resulting network may be very high. To overcome that disadvantage, this paper presents another generalization of the star g

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Divya Rashmi, S. V., A. Somasundaram, and S. Arumugam. "Secure domination subdivision number of a graph." Discrete Mathematics, Algorithms and Applications 11, no. 03 (2019): 1950036. http://dx.doi.org/10.1142/s1793830919500368.

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Let [Formula: see text] be a graph of order [Formula: see text] and size [Formula: see text] A dominating set [Formula: see text] of [Formula: see text] is called a secure dominating set if for each [Formula: see text] there exists [Formula: see text] such that [Formula: see text] is adjacent to [Formula: see text] and [Formula: see text] is a dominating set of [Formula: see text] In this case, we say that [Formula: see text] is [Formula: see text]-defended by [Formula: see text] or [Formula: see text] [Formula: see text]-defends [Formula: see text] The secure domination number [Formula: see t

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Favaron, O., H. Karami, and S. M. Sheikholeslami. "Game domination subdivision number of a graph." Journal of Combinatorial Optimization 30, no. 1 (2013): 109–19. http://dx.doi.org/10.1007/s10878-013-9636-6.

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Dvořák, Zdeněk. "On forbidden subdivision characterizations of graph classes." European Journal of Combinatorics 29, no. 5 (2008): 1321–32. http://dx.doi.org/10.1016/j.ejc.2007.05.008.

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