Some New Results on Seidel Equienergetic Graphs
1
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. Some variants of energy can also be found in the literature, in which the energy is de ned for the Laplacian matrix, Distance matrix, Common-neighbourhood matrix or Seidel matrix. The Seidel matrix of the graph G is the square matrix in which ijth entry is 1 or 1, if the vertices vi and vj are adjacent or non-adjacent respectively, and is 0 , if vi = vj . The Seidel energy of G is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some families of pairs of graphs whose Seidel matrices have di erent eigenvalues, but who have the same Seidel energies.
Abstract
The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. Some variants of energy can also be found in the literature, in which the energy is de ned for the Laplacian matrix, Distance matrix, Common-neighbourhood matrix or Seidel matrix. The Seidel matrix of the graph G is the square matrix in which ijth entry is 1 or 1, if the vertices vi and vj are adjacent or non-adjacent respectively, and is 0 , if vi = vj . The Seidel energy of G is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some families of pairs of graphs whose Seidel matrices have di erent eigenvalues, but who have the same Seidel energies.
참고문헌 (13)
- C. Adiga, "The skew energy of a digraph", Linear Algebra Appl, 432, pp.1825~1835 (2010)
- R. Balakrishnan, "A textbook of graph theory" (2000), Springer-Verlag
- S. B. Bozkurt, "Note on distance energy of graphs", MATCH Commun. Math. Comput. Chem, 64, pp.129~134 (2010)
- D. Cvetkovic, "An introduction to the theory of graph spectra" (2010), Cambridge university press
- I. Gutman, "The energy of a graph", Ber. Math. Statist. Sekt. Forsch. Graz, 103, pp.1~22 (1978)
- I. Gutman, "On incidence energy of a graph", Linear Algebra Appl, 431, pp.1223~1233 (2009)
- I. Gutman, "Laplacian energy of a graph", Linear Algebra Appl, 414, pp.29~37 (2006)
- W. H. Haemers, "Seidel switching and graph energy", MATCH Commun. Math. Comput. Chem, 68, pp.653~659 (2012)
- R. A. Horn, "Topics In matrix analysis" (1991), Cambridge University Press
- S. Lang, "Algebra" (2002), Springer-Verlag
- H. S. Ramane, "Seidel equienergetic graphs", Bulletin of Mathematical Sciences and Applications, 16, pp.62~69 (2016)
- H. S. Ramane, "Seidel energy of iterated line graphs of regular graphs", Kragujevac J. Math, 39(1), pp.7~12 (2015)
- X. Li, "Graph energy" (2012), Springer