THE NIRMALA’S MINIMUM DOMINATING ENERGY OF A GRAPH
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Published:
Jul 9, 2022
   Page:
14-21
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B. K. DIVYASHREE
Department of Mathematics, Government Science College, Bangalore, 560056, India.
R. JAGADEESH
Department of Mathematics, Government First Grade College, Ramanagara, 562120, India.
. SIDDABASAPPA
Department of Mathematics, Government Science College, Bangalore, 560056, India.
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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Original Research Article
References
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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.
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.