Minimal energies of trees with given parameters

作者：Zhu, Jianming^*

来源：Linear Algebra and Its Applications, 2012, 436(9): 3120-3131.

DOI：10.1016/j.laa.2011.10.002

• Energy
• Tree
• Domination number
• Matching number
• Independence number

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Let T(k) be the set of trees with given order k. Suppose that T is an element of T(k) and {v(1), v(2), ... , v(k)} be the ordering vertex set of T. We denote by T(n(1), n(2), ... , n(k)) the graph obtained by attaching n(i) pendent vertices to vertex v(i) (i = 1, 2, ... , k) of T respectively. Let T(n, k) = {T(n(1), n(2), ... , n(k)}|T is an element of T(k), n(1) + n(2) + ... + n(k) = n - k, n(i) >= 1, i = 1, 2, ... , k). In this paper, we determine the trees in T(n, k) with the first and the second minimal energies. As applications, we can characterize the trees with the first and the second minimal energies among the set of trees with given domination number, matching number, independence number respectively.

• 出版日期2012-5-1
• 单位同济大学; 上海对外经贸大学