IJPAM: Volume 114, No. 1 (2017)

Title

ON SPECTRA OF GLUED COMPLETE GRAPHS

Authors

C.Y. Jung$^1$, A.R. Nizami$^2$, M. Munir$^3$, W. Nazeer$^4$, S.M. Kang$^5$
$^{1}$Department of Business Administration
Gyeongsang National University
Jinju, 52828, KOREA
$^{2,3,4}$Department of Mathematics and Statistics
University of Lahore
Lahore, 54000, PAKISTAN
$^{5}$Department of Mathematics and RINS
Gyeongsang National University
Jinju, 52828, KOREA

Abstract

In this article, we give spectra and characteristic polynomial of three partite complete graphs. We also give spectra of cartesian and tenor product of $K_{n,n,n}$ with itself. Finally, we give general closed forms of the characteristic polynomials of the graphs obtained by identifying two copies of $K_n$ at a vertex and an edge.

History

Received: February 2, 2017
Revised: March 22, 2017
Published: April 21, 2017

AMS Classification, Key Words

AMS Subject Classification: 05C12
Key Words and Phrases: characteristic polynomial, eigenvalue, spectrum

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Bibliography

1
O. Ahmadi, N. Alon, I.F. Blake, I.E. Shparlinski, Graphs with integral spectrum, Linear Algebra Appl. 430 (2009), 547-552 doi: https://doi.org/10.1016/j.laa.2008.08.020.

2
N. Alon, Eigenvalues and expanders, Theory of computing (Singer Island, Fla., 1984), Combinatorica 6 (1986), 83-96, doi: https://doi.org/10.1007/BF02579166.

2
S. Axler, Linear Algebra Done Right, Second edition, Springer-Verlag, New York (1997).

2
H. Bai, The Grone-Merris Conjecture, arXiv:0911.2172 [math.CO].

2
E. Bannai, T. Ito, On finite Moore graphs, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 191-208.

2
E. Bannai, T. Ito, Algebraic Combinatorics I, Association Schemes, The Benjamin/Cummings Publishing Co., Inc., Menlo Park, CA (1984).

3
B. Bollobás, Modern Graph Theory, Graduate Texts in Mathematics, Springer-Verlag, New York, (1998).

4
A.E. Brouwer, W.H. Haemers, Spectra of Graphs, Springer, New York, (2012).

5
K. Bryan, T. Leise, The $25,000,000,000 eigenvector: the linear algebra behind Google, SIAM Rev. 48 (2006), 569-581, doi: https://doi.org/10.1137/050623280.

6
H. Chuang, G.R. Omidi, Graphs with three distinct eigenvalues and largest eigenvalues less than 8, Linear Algebra Appl. 430 (2009), 2053-2062, doi: https://doi.org/10.1016/j.laa.2008.11.028.

2
F.R.K. Chung, Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, 92. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, (1997).

2
S.M. Cioaba, Perfect matchings, eigenvalues and expansion, C. R. Math. Acad. Sci. Soc. R. Can. 27 (2005), 101-104.

7
D.M. Cvetković, Graphs and their spectra, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 354-356 (1971), 1-50.

8
D.M. Cvetković, M. Doob, H. Sachs, Spectra of Graphs, Theory and Applications, Third edition, Johann Ambrosius Barth, Heidelberg, (1995).

9
C.D. Godsil, Spectra of trees, Convexity and graph theory (Jerusalem, 1981), North-Holland Math. Stud. 87 (1984), 151-159, Ann. Discrete Math., 20, doi: https://doi.org/10.1016/S0304-0208(08)72819-6.

10
I. Gutman, P.J. Plath, On molecular graphs and digraphs of annulenes and their spectra, J. Serb. Chem. Soc. 66 (2001), 237-241.

11
M. Petri, Spectral properties of generalized direct product of graphs, Ph.D. Thesis, University of Novi Sad, (1994).

12
Ph. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl. 10 (1973), 163-170.

How to Cite?

DOI: 10.12732/ijpam.v114i1.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 114
Issue: 1
Pages: 105 - 111


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