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Title: Lexicographic polynomials of graphs and their spectra
Author: Cardoso, Domingos M.
Carvalho, Paula
Rama, Paula
Simic, Slobodan K.
Stanic, Zoran
Keywords: Spectral graph theory
Lexicographic product
Adjacency and Laplacian matrices
Cospectral graphs
Integral graphs
Issue Date: 24-Oct-2017
Publisher: University of Belgrade
Abstract: For a (simple) graph $H$ and non-negative integers $c_0,c_1,\ldots,c_d$ ($c_d \neq 0$), $p(H)=\sum_{k=0}^d{c_k \cdot H^k}$ is the lexicographic polynomial in $H$ of degree $d$, where the sum of two graphs is their join and $c_k \cdot H^k$ is the join of $c_k$ copies of $H^k$. The graph $H^k$ is the $k$th power of $H$ with respect to the lexicographic product ($H^0 = K_1$). The spectrum (if $H$ is regular) and the Laplacian spectrum (in general case) of $p(H)$ are determined in terms of the spectrum of $H$ and~$c_k$'s. Constructions of infinite families of cospectral or integral graphs are also announced.
Peer review: yes
DOI: https//10.2298/AADM1702258C
ISSN: 1452-8630
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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