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Adjacency matrices of semigraphs and their spectral analysis

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초록

We discuss Adjacency matrix and L-adjacency matrix representation of a semigraph and obtain Sach`s type theorems for semigraphs for interperting first few coefficients of the characteristic polynomial of the associated matrices in terms of semigraph parameters. We find the eigenvalues and their bounds certain classes of semigraphs. We define corresponding energies as the sum of the absolute values of the eigenvalues and also find the energy bounds.

Abstract

We discuss Adjacency matrix and L-adjacency matrix representation of a semigraph and obtain Sach`s type theorems for semigraphs for interperting first few coefficients of the characteristic polynomial of the associated matrices in terms of semigraph parameters. We find the eigenvalues and their bounds certain classes of semigraphs. We define corresponding energies as the sum of the absolute values of the eigenvalues and also find the energy bounds.

참고문헌 (14)

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  2. R. Balakrishnan, "A Text Book of Graph Theory" (2012), Springer
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  5. I. Gutman, "The energy of graphs", Ber. Math. Statist. Sekt. Forsch-ungszentram Graz, 103, pp.1~22 (1978)
  6. I. Gutman, "The energy of a graph, Old and New results, Algebraic combinatorics and applications" (2000), Springer
  7. S. S. Kamath, "Domination in Semigraphs", Electronic Notes in Discrete Mathematics, 15, pp.106~111 (2003)
  8. S. S. Kamath, "Strong and Weak Domination, and Domination Balence in Semigraphs", Electronic Notes in Discrete Mathematics, 15, pp.112~ (2003)
  9. K. Kayathri, "Coloring of Complete Semigraphs", Acta Cienc. Indica, Math, 33(2), pp.605~614 (2007)
  10. E. Sampathkumar, "Semigraphs and their applications, DST", MS, 94, pp.Department of Science and Technology, Govt. of India, New Delhi[DOI]
  11. E. Sampathkumar, "Matrix representation of semigraphs", Advanced Studies in Contemporary Mathematics, 14(1), pp.103~109 (2007), 장전수학회
  12. S. P. Subbaiah, "A study of graph theory: Topology, Steiner domination and Semigraph concepts", Ph.D., pp.2007
  13. Shambhulingaiah. K.S, "A Study of some topics in the theory of Semigraphs", Ph.D., pp.2010
  14. D. B. West, "Introduction to graph theory", pp.20~ (2005), PHI

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