THE NIRMALA’S MINIMUM DOMINATING ENERGY OF A GRAPH

B. K. DIVYASHREE; R. JAGADEESH; . SIDDABASAPPA

doi:10.56557/japsi/2022/v14i17759

THE NIRMALA’S MINIMUM DOMINATING ENERGY OF A GRAPH

B. K. DIVYASHREE

R. JAGADEESH

. SIDDABASAPPA

Journal of Applied Physical Science International, Page 14-21
DOI: 10.56557/japsi/2022/v14i17759
Published: 9 July 2022

Abstract

Nirmala index is one of the recently discovered topological index. It is originally a vertex based topological invariant and is defined as the sum of \(\sqrt{d(r)+d(s)}\) terms on all edges of the graph, where \(d(r)\) is the degree of the vertex \(r\) in \(G\) . In this paper we put forward a new energy called as the nirmala minimum dominating energy of a graph \(N E_{D}(G)\) . Also, we compute \(N E_{D}(G)\) for cocktail party graph, star graph, complete bipartite graph and complete graph. The estimation of upper and lower bounds for \(N E_{D}(G)\) are found.

Keywords:

Nirmala energy
nirmala’s minimum dominating energy
cocktail party graph
star graph
complete bipartite graph and complete graph

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How to Cite

DIVYASHREEB. K., JAGADEESHR., & SIDDABASAPPA. (2022). THE NIRMALA’S MINIMUM DOMINATING ENERGY OF A GRAPH. Journal of Applied Physical Science International, 14(1), 14-21. https://doi.org/10.56557/japsi/2022/v14i17759

References

Gutman I, The energy of a graph, Ber. Math-Statist. Sekt. Forschungsz. Graz. 1978;103:1-22.

Bondy JA, Murty USR, Graph Theory with Applications, Macmillan Press, New York. 1976;101-131.

Kulli V R,College Graph Theory,Vishwa International Publications, Gulbarga. 2012;53-62.

Wagner S, Wang H. Introduction to Chemical Graph Theory, CRC Press, Boca Raton. 2018;67-115.

Gutman I,“The energy of a graph”, Ber. Math-Statist. Sekt. Forschungsz. Graz. 1978;103:1-22.

Gutman I, Trinajsti N. Graph theory and molecular orbitals. Total p-electron energy of alternant hydrocarbons, Chemical Physics Letters. 1972;17:535-538.

Gutman I, Geometric approach to degree–based topological indices: Sombor indices, MATCH Comm. in Mathematical and in Computer Chemistry. 2021;86:11-16.

Gutman I. Some basic properties of Sombor indices, Open Journal of Discrete Applied Mathematics. 2021;4(1):1-3.

Kulli VR. Nirmala index, International Journal of Mathematics Trends and Technology. 2021;67(3):8-12.

Shao Y, Gao Y, Gao W, Zhao X. Degree–based energies of trees, Linear Algebra and Its Applications. 2021;621:18-28.

Kulli VR, K_1 and K_2 Indic, International Journal of Mathematics Trends and Technology. 2022;68(1):43-52.

Kulli VR. Banhatti-Nirmala Index of certain chemical networ, International Journal of Mathematics Trends and Technology. 2022;68(4):12-17.

Kulli VR, Gutman I. On some mathematical properties of Nirmala index, Annals of Pure and Applied Mathematics. 2021;23(2):93-99.

Cvetkovi´c D, Rowlinson P, Simi S. An Introduction to the Theory of Graph Spectra, Cambridge Univ. Press, Cambridge. 2010;7- 31.

Das KC, Gutman I, Milovanovi´c I, Milovanovi´c E, Furtula B. Degree–based energies of graphs”, Linear Algebra and Its Applications. 2018;554:185-204.

Li X, Wang Z. Trees with extremal spectral radius of weighted adjacency matrices among trees weighted by degree–based indices, Linear Algebra and Its Applications. 2021; 620:61-75.

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