• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2024, Volume: 17, Issue: 18, Pages: 1838-1844

Original Article

Minimum Degree Energy of Graphs and Pebbling Graphs

Received Date:15 March 2024, Accepted Date:09 April 2024, Published Date:25 April 2024


Objectives: The minimum degree energy concept is applied to pebbling graphs. This study establishes a connection between the minimum degree energy of graphs and the minimum degree energy of pebbling graphs by applying the lowest degree energy of pebbling notion to twenty standard graphs. Methods: The minimum degree energy of pebbling graph with the matrix whose was calculated using . The characteristic polynomial of the minimum degree, is must be found from the matrix. Next, the eigen values of the matrix were calculated using and the sum of all the eigen values gives the minimum degree energy. The lower and upper bounds for the minimum degree energy of graphs are established along with the algorithm for computing the minimum degree energy of graphs. Findings: The lower and upper bounds were found for the minimum degree energy of pebbling graphs. For twenty standard graphs and pebbling graphs, the minimum degree energy values were calculated, and their relation was tabulated. Novelty: Pebbling graphs were subjected to the minimal energy idea and a relationship was found between the minimum energy of pebbling graphs and the minimum energy of graphs in general.

Keywords: Energy, Minimum degree energy, Grotzsch graph, Pebbling graph, Data mining


  1. Erdös P. On pseudoprimes and Carmichael numbers. Publicationes Mathematicae Debrecen. 1956;4:201–206. Available from: https://publi.math.unideb.hu/load_doc.php?p=4120&t=abs
  2. Akram M, Sarwar M, Dudek WA. Energy of Bipolar Fuzzy Graphs . In: Graphs for the Analysis of Bipolar Fuzzy Information, Studies in Fuzziness and Soft Computing . (Vol. 401, pp. 309-347) Singapore. Springer. 2021.
  3. Philip AM, Kalayathankal SJ, Kureethara JV. On the Laplacian energy of interval valued fuzzy graphs. In: PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). (Vol. 2261, Issue 1) AIP Publishing. 2020.
  4. Srinivasan S, Shanmugavel V. Adjacency energy of pebbling graphs. In: International Conference on Mathematical Modeling and Computational Methods in Science and Engineering (ICMMCMSE-2020) , Journal of Physics: Conference Series. (Vol. 1850, pp. 1-11) IOP Publishing. 2021.
  5. Kotambari R, Jog S. Minimum Covering Maximum Degree Energy of a Graph. International Journal of Advanced Science and Engineering. 2020;7(2):1761–1769. Available from: https://dx.doi.org/10.29294/ijase.7.2.2020.1761-1769
  6. Rao KS, Saravanan K, Prakasha KN, Cangul IN. Maximum and Minimum degree energies of p-splitting and p-shadow graphs. TWMS Journal of Applied and Engineering Mathematics. 2022;12(1):1–10. Available from: https://jaem.isikun.edu.tr/web/images/articles/vol.12.no.1/01.pdf
  7. Zhang X, Bilal A, Munir MM, Rehman HMu. Maximum degree and minimum degree spectral radii of some graph operations. Mathematical Biosciences and Engineering. 2022;19(10):10108–10121. Available from: https://dx.doi.org/10.3934/mbe.2022473
  8. Surya SS, Mathew L. Secure Domination Cover Pebbling Number of Join of graphs. Indian Journal Of Science And Technology. 2022;15(27):1344–1348. Available from: https://dx.doi.org/10.17485/ijst/v15i27.2145
  9. Paul P, Fathima SSA. A Study on Edge Pebbling Number, Covering Cover Edge Pebbling Number of Friendship Graphs, Odd Path and Even Path. Indian Journal Of Science And Technology. 2023;16(32):2480–2484. Available from: https://dx.doi.org/10.17485/ijst/v16i32.674
  10. Isaak G, Prudente M. Two-player pebbling on diameter 2 graphs. International Journal of Game Theory. 2021;50(2):581–596. Available from: https://dx.doi.org/10.1007/s00182-021-00766-0
  11. Mathad V, Anand. The Maximum Hub Degree Energy of Graphs. International Journal of Applied Engineering Research. 2023;18(1):47–51. Available from: https://dx.doi.org/10.37622/ijaer/18.1.2023.47-51


© 2024 Srinivasan & Shanmugavel. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


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