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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 3 | Year 2023 | Article Id. IJMTT-V69I3P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I3P503

Degree Sum Energy in Context of Some Graph Operations on Regular Graph


Mitesh J. Patel, K. S. Baldaniya, Ashika Panicker
Received Revised Accepted Published
02 Feb 2023 03 Mar 2023 16 Mar 2023 27 Mar 2023
Abstract

Let G be a graph with order p and size q. The degree sum energy of a graph G is defined as the sum of the absolute values of the eigenvalues of the degree sum matrix of G. In this paper, we obtain the degree sum energy of m−splitting graph of a regular graph and central graph of regular graph. We define a new operation m−semishadow graph and obtain degree sum energy of m−semishadow graph of a regular graph.

Keywords
Degree sum energy, m-Splitting graph, m-Semishadow graph, Central graph, Regular graph.
References

[1] M.M. Ali Akbar, K. Kaliraj and Vernold J. Vivin, “On equitable coloring of central graphs and total graphs”, Electronic Notes in Discrete Mathematics, vol. 33, pp. 1-6, 2009.
[2] David W. Lewis, “Matrix Theory”, Allied Publishers Ltd, 1995.
[3] G. V. Ghodasara and M. J. Patel, “Some bistar related square sum graphs”, International Journal of Mathematics Trends and Technology, vol. 8, no. 1, pp. 47-57, 2013.
[4] H. S. Ramane, D. S. Revankar and J. B. Patil, “Bounds for the degree sum eigen values and degree sum energy of a graph”, International Journal of Pure and Applied Mathematical Sciences, vol. 6, no. 2, pp. 161-167, 2013.
[5] I. Gutman, The energy of a graph, Berlin Mathmatics-Statistics Forschungszentrum, vol. 103, pp. 1-22, 1978.
[6] I. Gutman, H. S. Ramane, “Research on Graph Energies in 2019”, MATCH Communications in Mathematical and in Computer Chemistry, vol. 84, pp. 277-292, 2020.
[7] I. Shparlinski, “On the energy of some circulant graphs”, Linear Algebra and its Applications, vol. 414, pp. 378-382, 2006.
[8] J. A. Bondy and U.S. Murty, “Graph Theory with Applications”, Elsevier Science Publication, 1982.
[9] M. J. Patel and G. V. Ghodasara, “Some Results on Degree Sum Energy of a Graph”, Recent Advancements in Graph Theory,CRC Press, pp. 1-7, 2017.
[10] S. Jog, R. Kotambari, “Degree Sum Energy of Some Graphs”, Annals of Pure and Applied Mathematics, vol. 11, pp. 17-27, 2016.
[11] S. K. Vaidya, K. M. Popat, “Energy of m-splitting and m-shadow graphs”, Far East Journal of Mathematical Sciences, vol. 102, pp. 571-1578, 2017.
[12] S. M. Hosamani, H. S. Ramane, “On Degree Sum Energy of a Graph”, European Journal of Pure and Applied Mathematics, vol. 9, no. 3, pp. 340-345, 2016.
[13] S. P. Hande, S. R. Jog and D. S. Revankar, “Bounds for the degree sum eigenvalue and degree sum energy of a common neighborhood graph”, International Journal of Graph Theory, vol. 1, no. 4, pp. 131-136, 2013.
[14] S. R. Jog, S. P. Hande and D. S. Revankar, “Degree sum polynomial of graph valued functions on regular graphs”, International Journal of Graph Theory, vol. 1, no. 3, pp. 108-115, 2013.

Citation :

Mitesh J. Patel, K. S. Baldaniya, Ashika Panicker, "Degree Sum Energy in Context of Some Graph Operations on Regular Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 3, pp. 16-25, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I3P503

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