SOME RECURRENCE RELATIONS FOR THE ENERGY OF CYCLE AND PATH GRAPHS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Energy of a graph, rst de ned by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix while searching for a method to obtain approximate solutions of Schrödinger equation for a class of organic molecules, is an important sub area of graph theory. This equation is a second order dierential equation which include the energy of the corresponding system. The energy of many graph types are well-known in literature. To know the energy of a molecule is an important aspect in Chemical Graph Theory. Two classes, cycles and paths, show serious dierences from others as the eigenvalues are trigonometric algebraic numbers which makes it difficult to calculate the energy of the corresponding graph. Here we obtain the polynomials and recurrence relations for the spectral polynomials of cycles and paths to nd the energy of larger graphs easier than the classical way.
Abstract
Energy of a graph, rst de ned by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix while searching for a method to obtain approximate solutions of Schrödinger equation for a class of organic molecules, is an important sub area of graph theory. This equation is a second order dierential equation which include the energy of the corresponding system. The energy of many graph types are well-known in literature. To know the energy of a molecule is an important aspect in Chemical Graph Theory. Two classes, cycles and paths, show serious dierences from others as the eigenvalues are trigonometric algebraic numbers which makes it difficult to calculate the energy of the corresponding graph. Here we obtain the polynomials and recurrence relations for the spectral polynomials of cycles and paths to nd the energy of larger graphs easier than the classical way.
참고문헌 (23)
- C. Adiga, "More graphs whose energy exceeds the number of vertices", Iranian Journal of Mathematical Sciences and Informatics, 2(2), pp.57~62 (2007)
- J. M. Aldous, "Graphs and Applications" (2004)
- R. Balakrishnan, "A Textbook of Graph Theory" (2012), Springer
- C. Berge, "The Theory of Graphs" (2001), Fletcher and Son Ltd
- N. L. Biggs, "Graph Theory. 1736-1936" (2001), Oxford University Press
- B. Bollobas, "Graduate Texts in Mathematics, Modern Graph Theory" (1998), Springer
- J. A. Bondy, "Graph Theory" (1998), Springer
- A. E. Brouwer, "Spectra of Graphs" (2012), Springer
- F. Celik, "Graphs and Graph Energy", pp.2016
- FERIHA CELIK, "Formulae and recurrence relations on spectral polynomials of some graphs", Advanced Studies in Contemporary Mathematics, 27(3), pp.325~332 (2017), 장전수학회[DOI]
- F. Celik, "On the Spectra of Cycles and Paths"
- W. Chen, "Applied Graph Theory" (1976), North-Holland Publishing Company
- D. Cvetkovic, "Spectra of Graphs-Theory and Applications" (1995), Academic Press
- L. R. Foulds, "Graph Theory Applications" (1992), Springer
- M. C. Golumbic, "Graph Theory. Combinatorics and Algorithms" (2005), Springer
- I. Gutman, "The Energy of a Graph", Ber. Math. Statist. Sekt. Forshungsz. Graz, 103, pp.1~22 (1978)
- F. Harary, "Graph Theory" (1994), Addison-Wesley
- J. M. Harris, "Combinatorics and Graph Theory" (2008), Springer
- E. Huckel, , Zeitschrift fur Physik, 70, pp.204~ (1933)
- X. Li, "Graph Energy" (2012), Springer
- V. Nikiforov, "The energy of graphs and matrices", J. Math. Anal. Appl., 326, pp.1472~1475 (2007)[DOI]
- H. B. Walikar, "Graph Connections", pp.120~123 (1999), Allied Publishers
- D. B. West, "Introduction to Graph Theory" (1996), Prentice Hall