ENERGY OF COMBINATORIAL MATRICES OF GRAPHS
Asian Journal of Mathematics and Computer Research,
Page 9-26
Abstract
Let G= (V, E) be a simple connected graph. In this paper, we have evaluated the energies of combinatorial matrices. We have two types of path defined matrices that is distance path and detour path the elements of these matrices are found combinatorially from the traditional distance and detour matrices. Here, we have calculated energies of standard graphs for both distance path and detour path matrices. Upper and lower bounds for these combinatorial matrices are also determined.
Keywords:
- Combinatorial matrices
- graphs
- energy
- matrix
How to Cite
DIVYASHREE, B. K., JAGADEESH, R., & SIDDABASAPPA, . (2022). ENERGY OF COMBINATORIAL MATRICES OF GRAPHS. Asian Journal of Mathematics and Computer Research, 29(1), 9-26. Retrieved from https://www.ikprress.org/index.php/AJOMCOR/article/view/7574
References
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Mircea V. Diudea, Gabriel Katona, Istvan Lukovits Acta, Nenad Trinajstic. Detour and cluj-detour indices. , Croat. Chem. Acta. 1998;71:459-471.
Gutman I, Polansky OE. Mathematical concepts in organic chemistry, Springer–Verlag, Berlin; 1986.
Cvetkovi´c D, Gutman I (Eds.). Selected Topics on Applications of Graph Spectra, Math. Inst., Belgrade; 2011.
Cvetković D, Gutman I. The computer system GRAPH: A useful tool in chemical graph theory. J. Comput. Chem. 1986;7:640–644.
Gutman I, Li X, Zhang J. In analysis of complex networks. From Biology to Linguistics, M. Dehmer, F. Emmert-Streib, Eds., Wiley-VCH: Weinheim. 2009;145.
Mircea V. Diudea. Walk Numbers 〖e_M〗^W: Wiener-Type Numbers of Higher Rank, Journal of Chemical Information and Computer Sciences. 1996;36(3):535-540.
Yu A, Lu M, Tian F. New upper bounds for the energy of graphs. MATCH Commun. Math. Comput. Chem. 2005;53:441–458.
McClelland BJ. Properties of the latent roots of a matrix: The estimation of π-electron energies. J. Chem. Phys. 1971;54:640-643.
Graovac A, Gutman I, Trinajsti´c N. Topological approach to the chemistry of conjugated molecules. Springer–Verlag, Berlin; 1977.
Gutman I. The energy of a graph: Old and new results, in: A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer–Verlag, Berlin. 2001;196–211.
Mircea V. Diudea, Gabriel Katona, Istvan Lukovits Acta, Nenad Trinajstic. Detour and cluj-detour indices. , Croat. Chem. Acta. 1998;71:459-471.
Gutman I, Polansky OE. Mathematical concepts in organic chemistry, Springer–Verlag, Berlin; 1986.
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