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Relevant bibliographies by topics / Degree splitting graph

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Academic literature on the topic 'Degree splitting graph'

Author: Grafiati

Published: 3 June 2025

Last updated: 19 July 2025

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Journal articles on the topic "Degree splitting graph"

1

Basavanagoud, B., and Roopa S. Kusugal. "On the Line Degree Splitting Graph of a Graph." Bulletin of Mathematical Sciences and Applications 18 (May 2017): 1–10. http://dx.doi.org/10.18052/www.scipress.com/bmsa.18.1.

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In this paper, we introduce the concept of the line degree splitting graph of a graph. We obtain some properties of this graph. We find the girth of the line degree splitting graphs. Further, we establish the characterization of graphs whose line degree splitting graphs are eulerian, complete bipartite graphs and complete graphs.

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2

Zhang, Xiujun, Ahmad Bilal, M. Mobeen Munir, and Hafiz Mutte ur Rehman. "Maximum degree and minimum degree spectral radii of some graph operations." Mathematical Biosciences and Engineering 19, no. 10 (2022): 10108–21. http://dx.doi.org/10.3934/mbe.2022473.

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<abstract><p>New results relating to the maximum and minimum degree spectral radii of generalized splitting and shadow graphs have been constructed on the basis of any regular graph, referred as base graph. In particular, we establish the relations of extreme degree spectral radii of generalized splitting and shadow graphs of any regular graph.</p></abstract>

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3

Dominic, Charles. "Zero forcing number of degree splitting graphs and complete degree splitting graphs." Acta Universitatis Sapientiae, Mathematica 11, no. 1 (2019): 40–53. http://dx.doi.org/10.2478/ausm-2019-0004.

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Abstract A subset ℤ ⊆ V(G) of initially colored black vertices of a graph G is known as a zero forcing set if we can alter the color of all vertices in G as black by iteratively applying the subsequent color change condition. At each step, any black colored vertex has exactly one white neighbor, then change the color of this white vertex as black. The zero forcing number ℤ (G), is the minimum number of vertices in a zero forcing set ℤ of G (see [11]). In this paper, we compute the zero forcing number of the degree splitting graph (𝒟𝒮-Graph) and the complete degree splitting graph (𝒞𝒟𝒮-Graph) of a graph. We prove that for any simple graph, ℤ [𝒟𝒮(G)] k + t, where ℤ (G) = k and t is the number of newly introduced vertices in 𝒟𝒮(G) to construct it.

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Ibrahim, Arooj, and Saima Nazeer. "On Maximum Degree and Maximum Reverse Degree Energies of Splitting and Shadow graph of Complete graph." Utilitas Mathematica 119, no. 1 (2024): 73–82. http://dx.doi.org/10.61091/um119-08.

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In this paper, the relations of maximum degree energy and maximum reserve degree energy of a complete graph after removing a vertex have been shown to be proportional to the energy of the complete graph. The results of splitting the graph and shadow graphs are also presented for the complete graph after removing a vertex.

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Mirajkar, Keerthi G., and Y. B. Priyanka. "The Sum Degree Distance and the Product Degree Distance of Generalized Transformation Graphs G^ab." Bulletin of Mathematical Sciences and Applications 16 (August 2016): 76–88. http://dx.doi.org/10.18052/www.scipress.com/bmsa.16.76.

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In this contribution, we consider line splitting graph LS(G) of a graph G as transformation graph G++ of Gab. We investigate the sum degree distance DD+(G) and product degree distance DD*(G) of transformation graph Gab, which are weighted version of Wiener index. The Transformation graphs of Gab are G++, G+-, G-+ and G--.

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6

Anitha, J., and S. Muthukumar. "Power domination in splitting and degree splitting graph." Proyecciones (Antofagasta) 40, no. 6 (2021): 1641–55. http://dx.doi.org/10.22199/issn.0717-6279-4357-4641.

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A vertex set S is called a power dominating set of a graph G if every vertex within the system is monitored by the set S following a collection of rules for power grid monitoring. The power domination number of G is the order of a minimal power dominating set of G. In this paper, we solve the power domination number for splitting and degree splitting graph.

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7

Falcón, Raúl M., Venkitachalam Aparna, and Nagaraj Mohanapriya. "Optimal secret share distribution in degree splitting communication networks." Networks and Heterogeneous Media 18, no. 4 (2023): 1713–46. http://dx.doi.org/10.3934/nhm.2023075.

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<abstract><p>Dynamic coloring has recently emerged as a valuable tool to optimize cryptographic protocols based on secret sharing, which enforce data security in communication networks and have significant importance in both online storage and cloud computing. This type of graph labeling enables the dealer to distribute secret shares among the nodes of a communication network so that everybody can recover the secret after a minimum number of rounds of communication. This paper delves into this topic by dealing with the dynamic coloring problem for degree splitting graphs. The topological structure of the latter enables the dealer to avoid dishonesty by adding control nodes that supervise all those participants with a similar influence in the network. More precisely, we solve the dynamic coloring problem for degree splitting graphs of any regular graph. The irregular case is partially solved by establishing a lower bound for the corresponding dynamic chromatic number. As illustrative examples, we solve the dynamic coloring problem for the degree splitting graphs of cycles, cocktail, book, comb, fan, jellyfish, windmill and barbell graphs.</p></abstract>

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8

Kaneria, V. J., and J. M. Shah. "ABSOLUTE MEAN GRACEFUL LABELING IN THE CONTEXT OF m-SPLITTING AND DEGREE SPLITTING GRAPHS." South East Asian J. of Mathematics and Mathematical Sciences 19, no. 03 (2023): 359–70. http://dx.doi.org/10.56827/seajmms.2023.1903.28.

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A graph G with q edges is said to be absolute mean graceful if there is a one-to-one function f from V (G) to the set {0,±1,±2,±3,...,±q} such that when each edge xy is assigned the label |f(x)−f(y)| 2 , then the resulting edge labels are distinct. In this paper, the absolute mean graceful labeling of m-splitting and degree splitting graphs of some graphs are investigated.

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Kalaivani, R., and D. Vijayalakshmi. "On dominator coloring of degree splitting graph of some graphs." Journal of Physics: Conference Series 1139 (December 2018): 012081. http://dx.doi.org/10.1088/1742-6596/1139/1/012081.

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Mohanappriya, G., and D. Vijayalakshmi. "Degree based topological invariants of splitting graph." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 68, no. 2 (2019): 1341–49. http://dx.doi.org/10.31801/cfsuasmas.526546.

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Book chapters on the topic "Degree splitting graph"

1

Rao, K. Srinivasa, B. Amudha, and Ismail Naci Cangul. "A Note on Degree-Based Energies of m-Splitting and m-Shadow Graphs." In Advances in Intelligent Systems and Computing. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-8054-1_22.

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Conference papers on the topic "Degree splitting graph"

1

Priya, S. Banu, A. Parthiban, and N. Srinivasan. "Equitable power domination number of the degree splitting graph of certain graphs." In SECOND INTERNATIONAL CONFERENCE OF MATHEMATICS (SICME2019). Author(s), 2019. http://dx.doi.org/10.1063/1.5097514.

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