On the spectral radius of $‡$-shape trees

Ma, Xiaoling, and Wen, Fei. "On the spectral radius of $\ddag $-shape trees." Czechoslovak Mathematical Journal 63.3 (2013): 777-782. <http://eudml.org/doc/260715>.

@article{Ma2013,
abstract = {Let $A(G)$ be the adjacency matrix of $G$. The characteristic polynomial of the adjacency matrix $A$ is called the characteristic polynomial of the graph $G$ and is denoted by $\phi (G, \lambda )$ or simply $\phi (G)$. The spectrum of $G$ consists of the roots (together with their multiplicities) $\lambda _1(G)\ge \lambda _2(G)\ge \ldots \ge \lambda _n(G)$ of the equation $\phi (G, \lambda )=0$. The largest root $\lambda _1(G)$ is referred to as the spectral radius of $G$. A $\ddag $-shape is a tree with exactly two of its vertices having maximal degree 4. We will denote by $G(l_1, l_2, \ldots , l_7)$$(l_1\ge 0$, $l_i\ge 1$, $i=2,3,\ldots , 7)$ a $\ddag $-shape tree such that $G(l_1, l_2, \ldots , l_7)-u-v=P_\{l_1\}\cup P_\{l_2\}\cup \ldots \cup P_\{l_7\}$, where $u$ and $v$ are the vertices of degree 4. In this paper we prove that $3\sqrt\{2\}/\{2\}< \lambda _1(G(l_1, l_2, \ldots , l_7))< \{5\}/\{2\}$.},
author = {Ma, Xiaoling, Wen, Fei},
journal = {Czechoslovak Mathematical Journal},
keywords = {spectra of graphs; spectral radius; $\ddag $-shape tree; spectra of graphs; spectral radius; -shape tree},
language = {eng},
number = {3},
pages = {777-782},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the spectral radius of $\ddag $-shape trees},
url = {http://eudml.org/doc/260715},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Ma, Xiaoling
AU - Wen, Fei
TI - On the spectral radius of $\ddag $-shape trees
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 777
EP - 782
AB - Let $A(G)$ be the adjacency matrix of $G$. The characteristic polynomial of the adjacency matrix $A$ is called the characteristic polynomial of the graph $G$ and is denoted by $\phi (G, \lambda )$ or simply $\phi (G)$. The spectrum of $G$ consists of the roots (together with their multiplicities) $\lambda _1(G)\ge \lambda _2(G)\ge \ldots \ge \lambda _n(G)$ of the equation $\phi (G, \lambda )=0$. The largest root $\lambda _1(G)$ is referred to as the spectral radius of $G$. A $\ddag $-shape is a tree with exactly two of its vertices having maximal degree 4. We will denote by $G(l_1, l_2, \ldots , l_7)$$(l_1\ge 0$, $l_i\ge 1$, $i=2,3,\ldots , 7)$ a $\ddag $-shape tree such that $G(l_1, l_2, \ldots , l_7)-u-v=P_{l_1}\cup P_{l_2}\cup \ldots \cup P_{l_7}$, where $u$ and $v$ are the vertices of degree 4. In this paper we prove that $3\sqrt{2}/{2}< \lambda _1(G(l_1, l_2, \ldots , l_7))< {5}/{2}$.
LA - eng
KW - spectra of graphs; spectral radius; $\ddag $-shape tree; spectra of graphs; spectral radius; -shape tree
UR - http://eudml.org/doc/260715
ER -