Hypoenergetic and strongly hypoenergetic trees

Xueliang Li; Hongping Ma

Hypoenergetic and strongly hypoenergetic trees

Combinatorics 2009-05-26 v2

Authors: Xueliang Li , Hongping Ma

Abstract

The energy $E(G)$ of a graph $G$ is defined as the sum of the absolute values of the eigenvalues of $G$ . An $n$ -vertex graph is said to be hypoenergetic if $E(G)<n$ and strongly hypoenergetic if $E(G)<n-1$ . In this paper, we consider hypoenergetic and strongly hypoenergetic trees. For any given $n$ and $\Delta$ , the existence of both hypoenergetic and strongly hypoenergetic trees of order $n$ and maximum degree $\Delta$ is completely characterized.

Keywords

graph energy trees graph theory

Cite

@article{arxiv.0905.3944,
  title  = {Hypoenergetic and strongly hypoenergetic trees},
  author = {Xueliang Li and Hongping Ma},
  journal= {arXiv preprint arXiv:0905.3944},
  year   = {2009}
}