|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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