Laplacian coefficients of trees with a given bipartition
نویسندگان
چکیده
منابع مشابه
Lexicographical ordering by spectral moments of trees with a given bipartition
Lexicographic ordering by spectral moments ($S$-order) among all trees is discussed in this paper. For two given positive integers $p$ and $q$ with $pleqslant q$, we denote $mathscr{T}_n^{p, q}={T: T$ is a tree of order $n$ with a $(p, q)$-bipartition}. Furthermore, the last four trees, in the $S$-order, among $mathscr{T}_n^{p, q},(4leqslant pleqslant q)$ are characterized.
متن کاملlexicographical ordering by spectral moments of trees with a given bipartition
lexicographic ordering by spectral moments ($s$-order) among all trees is discussed in this paper. for two given positive integers $p$ and $q$ with $pleqslant q$, we denote $mathscr{t}_n^{p, q}={t: t$ is a tree of order $n$ with a $(p, q)$-bipartition}. furthermore, the last four trees, in the $s$-order, among $mathscr{t}_n^{p, q},(4leqslant pleqslant q)$ are characterized.
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k=0 (−1)n−k ck(T ) λk . Then, as well known, c0(T ) = 0 and c1(T ) = n . If T differs from the star (Sn) and the path (Pn), which requires n ≥ 5 , then c2(Sn) < c2(T ) < c2(Pn) and c3(Sn) < c3(T ) < c3(Pn) . If n = 4 , then c3(Sn) = c3(Pn) . AMS Mathematics Subject Classification (2000): 05C05, 05C12, 05C50
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Let F ⊂ K be fields of characteristic 0, and let K[x] denote the ring of polynomials with coefficients in K. Let p(x) = n ∑ k=0 akx k ∈ K[x], an 6= 0. For p ∈ K[x]\F [x], define DF (p), the F deficit of p, to equal n −max{0 ≤ k ≤ n : ak / ∈ F}. For p ∈ F [x], define DF (p) = n. Let p(x) = n ∑ k=0 akx k, q(x) = m ∑ j=0 bjx j , with an 6= 0, bm 6= 0, an, bm ∈ F , bj / ∈ F for some j ≥ 1. Suppose ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.01.011