### Atom Connectivity and Connectivity Energy of few Molecules

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Basak. S. C and V.R. Magnuson V. R, Determining structural similarity of chemicals using graph-theoretic indices, Discrete Applied Mathematics 19,17-44,1988.

B. Zhou, On the largest eigenvalues of the distance matrix of a tree, MATCH Commun. Math. Comput. Chem. 58, 657-662, 2007.

C. A. Coulson, On the calculation of the energy in unsaturated hydrocarbon molecules, Proc. Cambridge Phil. Soc., 36, 201 - 203,1940.

Danail Bonchev and Douglas J. Klein, On the Wiener Number of Thorn Trees, Stars, Rings, and Rods, CROATICA CHEMICA ACTA, CCACAA 75 (2) 613-620, 2002.

D.M.Cvetkovic, M.Doob, and H. Sachs, Spectra of graphs theory and applications, Academic press, New York, 1980.

E. Sampath Kumar, Graphs and Matrices, Proceedings of National Workshop on Graph theory Applied to chemistry, chapter-2, Centre for Mathematical Sciences, Pala Campus , Kerala, 1-3 Feb, 2010.

Frank. Harary, Graph theory, Addison Wiley, Reading Mass, 1975.

Gutman and Boris Furtula, Survey of Graph Energies, Mathematics Interdisciplinary Research 2, 85 – 129, 2017.

Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forschungszenturm Graz., 103, 1-22, 1978.

Gutman, O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, 1986.

Gutman, The energy of a graph: old and new results, Algebraic Combinatorics and Applications, Springer, 196-211, 2000.

Gutman, Topology and stability of conjugated hydrocarbons. The dependence of total ¼-electron energy on molecular topology, J. Serb. Chem. Soc., 70 441-456, 2005.

G. Indulal, I.Gutman, A.Vijaya Kumar On Distance Energy of a graph, MATCH Commun. Math. Comput. Chem. 60, 461-472, 2008.

Gutman, Sekt. Forchungsz, J.A. de la Pena and J. Rada, On the energy of regualr graphs, MATCH Commun. Math. Comput. Chem., 57, 351-361, 2007.

H.B. Walikar, The energy of a graph: Bounds, Graph theory Lecture notes , Department of Computer Science, Karnatak University, Dharwad, 2007.

H.S. Ramane, D.S. Revankar, Ivan Gutman, Siddani Bhaskara rao, B.D. Acharya, H.B. Walikar, Estimating the distance energy of graphs, Graph theory notes of New York LV, 2008.

H.S. Ramane, H.B. Walikar, S.B rao, B.D. Acharya, P.R. Hampiholi, S.R. Jog and Gutman, Spectra and energies of iterated line graphs of regular graphs, Appl. Math. Lett., 18, 679-682, 2005.

H.Hua and M.Wang, Unicyclic with given number of vertices and minimal energy, Lin. Algebra Appl., 426, 478-489, 2007.

Kamal Kumar. M, Domination energy of graphs, International Journal of Applied Mathematics, Vol. 3, No. 1, 417-424, 2012.

Kamal Kumar. M, Relation between domination number, energy of graph and rank. International Journal of Mathematics and Scientific Computing, 1(1), 58-61, 2011.

Kamal Kumar. M , Characteristic polynomial and domination energy of some special class of graphs. International Journal of Mathematical and Combinatorics, 1(1), 37-48, 2014.

Kamal Kumar. M, Johnson J..J, Winson. R, Different Domination energies in graphs, International Journal of Mathematical and Combinatorics, Vol.4, 103-145 , 2018.

Kamal Kumar. M, Shajidmon Kolamban, Various Domination energies in graphs, International Journal of Mathematical and Combinatorics, Vol. 3, No.12, 108-12, 2018.

M. Kamal Kumar, Shajidmon Kolamban, Bushra Hibras Al Sulaimi, The Energy of Graph –“A New Perspective”, Proceedings of International Conference( Virtual) on Interdisciplinary Research on Applied Science, Management and Technology (ICIRASMT), India, May 26-27, 2022.

M. Kamal Kumar, Shajidmon Kolamban, Bushra Hibras Al Sulaimi, THE ENERGY OF GRAPH: A NEW PERSPECTIVE, Global Journal of Modeling and Intelligent Computing, Vol. 2, No. 2, 2022.

Koolen. J. H, Moulton. V, Maximal energy graph, Adv. Appl. Math. 26,47-52, 2001.

Koolen. J. H, Moulton. V, Maximal energy of bipartite graph, Graphs Combin. 19, 131-35, 2003.

L.Ye and X. Yuan, On the minimal energies of trees with a given number of pendent vertices, MATCH Commun. Math. Comput. Chem., 57, 197-201, 2007.

Massoud Malek , Linear Algebra-Characteristic Polynomial, California State University, East Bay, Pg -5, 2008.

Mathavi Manisekar, S. Lalitha A Comparison between the Adjacency Matrix Energy and Dissociation Energy for Amino Acids, International Journal of Engineering Technology, Management and Applied Sciences, Volume 3, Issue 8. August 2015.

Spialter. L, The atom connectivity matrix (ACM) and its characteristic polynomial (ACMCP): A new computer-oriented chemical nomenclature, J. Am. Chem. Soc. 85, 2012-2013, 1963.

Spialte. L, The Atom Connectivity Matrix (ACM) and Its Characteristic Polynomial (ACMCP), J. Chem. Doc. 4 pp., 261-269, 1964.

Spialter. L, The Atom Connectivity Matrix Characteristic Polynomial (ACMCP) and Its Physico-Geometeric (Topological) Significance, J. Chem. Doc. 4 pp., 269-274, 1964.

Tamara Anthony Carter, Richard A. Tapia, Anne Papakonstantinou, An Introduction to Linear Algebra for Pre-Calculus Students, CEEE, 1995.

V. Nikiforov, The energy of graphs and matrices. J.Math. Anal. Appl., 326, 1472-75, 2007.

V. Nikiforov, Graphs and matrices with maximal energy. J.Math. Anal. Appl., 327, 735-738, 2007.

DOI: http://dx.doi.org/10.21533/scjournal.v13i1.303

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