- Tytuł:
- The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number
- Autorzy:
-
Su, Li
Li, Hong-Hai
Zhang, Jing - Powiązania:
- https://bibliotekanauki.pl/articles/30148000.pdf
- Data publikacji:
- 2014-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
clique number
kite graph
signless Laplacian
spectral radius - Opis:
- In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph $PK_{n-\omega,\omega}$ among all connected graphs with $n$ vertices and clique number $\omega$. In addition, we show that the spectral radius $\mu$ of $PK_{m,\omega}$ $(m\geq1)$ satisfies $$\frac{1}{2}(2\omega-1+\sqrt{4\omega^{2}-12\omega+17})\leq\mu\leq 2\omega-1.$$ More precisely, for $m>1$, $\mu$ satisfies the equation \[ \mu-\omega-\frac{\omega-1}{\mu-2\omega+3}=a_m\sqrt{\mu^2-4\mu}+\frac{1}{t_1}, \] where $a_m=\frac{1}{1-t_1^{2m+3}}$ and $t_{1}=\frac{\mu-2+\sqrt{(\mu-2)^{2}-4}}{2}$. At last the spectral radius $\mu(PK_{\infty,\omega})$ of the infinite graph $PK_{\infty,\omega}$ is also discussed.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2014, 34, 1; 95-102
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł