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http://hdl.handle.net/10773/18640
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 |
URI: | http://hdl.handle.net/10773/18640 |
DOI: | https//10.2298/AADM1702258C |
ISSN: | 1452-8630 |
Appears in Collections: | CIDMA - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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AADM-Vol11-No2-258-272.pdf | Main article | 392.94 kB | Adobe PDF | View/Open |
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