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- W1991418932 abstract "Let G be a bipartite graph with n vertices and m edges. Let S(G) be the subdivision of G, obtained by inserting a new vertex on each edge of G. The ordinary characteristic polynomial of S(G) and the Laplacian characteristic polynomial of G are related as φ(S(G),λ) = λm−nψ(G,λ2). If μi, i=1,2, … ,h, are the non-zero Laplacian eigenvalues of G, then the ordinary spectrum of S(G) consists of the numbers , and of n+m−2h zeros. As a corollary, we demonstrate that if ψ (G,λ) is written in the form , then for any tree T of order n and for any k, ck(Sn)≤ ck(T) ≤ ck(Pn), where Sn and Pn are, respectively, the star and the path of order n." @default.
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- W1991418932 date "2008-05-01" @default.
- W1991418932 modified "2023-09-27" @default.
- W1991418932 title "A connection between ordinary and Laplacian spectra of bipartite graphs" @default.
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- W1991418932 doi "https://doi.org/10.1080/03081080601002254" @default.
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