On the Laplacian spectra of product graphs | Zendy

Sasmita Barik | Zendy; R.B. Bapat | Zendy; Sukanta Pati | Zendy

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On the Laplacian spectra of product graphs

Author(s) -

Sasmita Barik,

R.B. Bapat,

Sukanta Pati

Publication year - 2015

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm150218006b

Subject(s) - cartesian product , mathematics , graph product , lexicographical order , algebraic connectivity , eigenvalues and eigenvectors , laplace operator , laplacian matrix , product (mathematics) , combinatorics , indifference graph , gramian matrix , discrete mathematics , graph , chordal graph , 1 planar graph , mathematical analysis , physics , geometry , quantum mechanics

Graph products and their structural properties have been studied extensively by many researchers. We investigate the Laplacian eigenvalues and eigenvectors of the product graphs for the four standard products, namely, the Cartesian product, the direct product, the strong product and the lexicographic product. A complete characterization of Laplacian spectrum of the Cartesian product of two graphs has been done by Merris. We give an explicit complete characterization of the Laplacian spectrum of the lexicographic product of two graphs using the Laplacian spectra of the factors. For the other two products, we describe the complete spectrum of the product graphs in some particular cases. We supply some new results relating to the algebraic connectivity of the product graphs. We describe the characteristic sets for the Cartesian product and for the lexicographic product of two graphs. As an application we construct new classes of Laplacian integral graphs.

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