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

Received | Revised | Accepted | Published |
---|---|---|---|

02 Feb 2023 | 03 Mar 2023 | 16 Mar 2023 | 27 Mar 2023 |

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.

[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.

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