Authors: Cardoso, Domingos
Carvalho, Paula
Rama, Paula
Simić, Slobodan 
Stanić, Zoran
Title: Lexicographic polynomials of graphs and their spectra
Journal: Applicable Analysis and Discrete Mathematics
Volume: 11
Issue: 2
First page: 258
Last page: 272
Issue Date: 1-Jan-2017
Rank: M22
ISSN: 1452-8630
DOI: 10.2298/AADM1702258C
Abstract: 
For a (simple) graph H and non-negative integers c0; c1; ... ; cd (cd ≠ 0), p(H) =Σkd=0 ck . Hk is the lexicographic polynomial in H of degree d, where the sum of two graphs is their join and ck . Hk is the join of ck copies of Hk. The graph Hk is the kth power of H with respect to the lexicographic product (H0 = K1). The spectrum (if H is connected and regular) and the Laplacian spectrum (in general case) of p(H) are determined in terms of the spectrum of H and ck's. Constructions of infinite families of cospectral or integral graphs are announced.
Keywords: Adjacency matrix | Cospectral graphs | Integral graphs | Laplacian matrix | Lexicographic product
Publisher: School of Electrical Engineering, University of Belgrade
Project: CIDMA - Center for Research and Development in Mathematics and Applications, Project UID/MAT/04106/2013
Geometry, Education and Visualization With Applications 
Graph theory and mathematical programming with applications in chemistry and computer science 

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