Minimum mean covering Gutman energy of certain graphs

Rao, M. V. Chakradhara; Lakshmi, D. Venkata; Srimannarayana, N.; Venkatesh, K. A.

doi:10.47974/JIM-1648

Open Access Research Article

Minimum mean covering Gutman energy of certain graphs

^*M. V. Chakradhara RaoCorresponding authorchakrimv@yahoo.comDepartment of Mathematics Presidency University Yelahanka Bangalore IndiaDepartment of Computer Applications Vidya Vikas Educational Trust First Grade CollegeMysore, Karnataka, 570028, IndiaView full profile → , D. Venkata LakshmiSchool of Computer Science and Engineering VIT-AP University Amaravati Andhra Pradesh IndaView full profile → , N. Srimannarayanasriman72@gmail.comDepartment of Mathematics Koneru Lakshmaiah Education Foundation Vaddeswaram Andhra Pradesh IndiaDepartment of Engineering Mathematics Koneru Lakshmaiah Education Foundation Vaddeswaram Guntur (Dt.,), Andhra Pradesh, IndiaView full profile → , K. A. Venkateshka.venkatesh@alliance.edu.inDepartment of Mathematics and Computer Science Myanmar Institute of Information Technology Mandalay Myanmar (Burma)Department of Computer Science Alliance UniversityBangalore West, Karnataka, IndiaView full profile →

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pp. 67–76Vol. 26Issue 1January 2023DOI: 10.47974/JIM-1648XML

Published Online:: 31 Jan 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1648
Pages:: 67–76

Abstract

The ᶆean-energy orᵯ-energy of a graph was introduced by Laura Buggy, Amaliailiuc, Katelyn Mc.Call, Duyguyen in 2010. The minimum mean covering energy (MMCE) is a special type of graph energy, symbolically represented by ( ), c E G introduced by C. Adiga et. al. The sum of the magnitudes of the characteristic values obtained from the Gutman matrix is named as Gutman energy. we present the results of minimum mean covering Gutman energies (MMCGE) of certain standard graphs (())MCGEG and the lower and upper bounds of ()MCGEG were also established.

Keywords

Gutman energy Minimum mean covering energy Minimum mean covering Gutman energy

Subject Classifications

05C5005C99

References

[1] C.Adiga, A. Bayad, I. Gutman, S. A. Srinivas, The minimum covering energy of a graph, Kragujevac Journal Science, 34, 39-56 (2012).
[2] I. Gutman, The energy of a graph, Ber. Math- Statist. Sekt. Forschungsz. Graz, 103, 1-22 (1978).
[3] M.V. ChakradharaRao,K.A.Venkatesh, D.V. Lakshmi, The Minimum Mean Monopoly Energy of Graphs, TWMS Journal of Applied and Engineering Mathematics Isik University, Department of Mathematics V. 11, Special Issue, pp. 144-153 (2021).
[4] M.V. ChakradharaRao,K.A.Venkatesh, N.Srimannarayana, D.V. Lakshmi,The Minimum Mean Hub Energy, ADV MATH SCI JOURNAL, Advances in Mathematics: Scientific Journal 9, No .9, 6809–6816 (2020). ISSN: 1857-8365 (printed); 1857-8438.
[5] Roshan Sara Philipose, Sarasija, P. B. Gutman Matrix and Gutman Energy of a Graph. Mathematical Sciences International Research Journal [Special Issue], Vol. 7, 63-66 (2018).
[6] Mario Gionfriddo, A remarkable connection between k-permutations and colourings of Graphs, Journal of Interdisciplinary Mathematics, Volume 14, Issue 1, 95-104 (2011). https://doi.org/10.1080/09720502.2011.10700737.
[7] Huiming Duan, Yixin Liu, Kun Wang and Meilin You, On connected m multiply 2 dimensions hyperplane complete residual graph, Journal of Interdisciplinary Mathematics, Volume 19, Issue 4, 811-821 (2016). https://doi.org/10.1080/09720502.2016.1191177.
[8] PintuBhunia, Santanu Bag and Kallol Paul, Bounds for eigen values of the adjacency matrix of a graph, Journal of Interdisciplinary Mathematics, Volume 22, Issue 4, 415-431 (2019). https://doi.org/10.1080/09720502.2019.1630938.

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