Minimal energies of trees with given parameters
نویسندگان
چکیده
منابع مشابه
Ela on Minimal Energies of Trees with given Diameter∗
The energy of G, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G. In this paper, the trees with a given diameter having the minimal energy are determined by three specific tree operations; using this method, together with previous work, a conjecture proposed by B. Zhou and F. Li [J. Math. Chem., 39:465–473, 2006] is completely solved.
متن کاملOn minimal energies of trees with given diameter
The energy of G, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G. In this paper, the trees with a given diameter having the minimal energy are determined by three specific tree operations; using this method, together with previous work, a conjecture proposed by B. Zhou and F. Li [J. Math. Chem., 39:465–473, 2006] is completely solved.
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The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Zhang et al (Discrete Appl. Math., 92(1999), 71-84) characterized the trees with a perfect matching having the minimal and the second minimal energies, which solved a conjecture proposed by Gutman (J. Math. Chem., 1(1987), 123-143). In this letter, for a given positive integer d we characterize t...
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A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. We prove that for a given nullity more than 1, there are only finitely many integral trees. It is also shown that integral trees with nullity 2 and 3 are unique.
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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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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.10.002