The minimum spectral radius of graphs with a given domination number
نویسندگان
چکیده
Let Gn,γ be the set of simple and connected graphs on n vertices with domination number γ. The graph minimum spectral radius among is called minimizer graph. In this paper, we first prove that must a tree. Moreover, for γ∈{1,2,3,⌈n3⌉,⌊n2⌋}, characterize all in Gn,γ.
منابع مشابه
The minimum spectral radius of graphs with a given clique number
In this paper, it is shown that among connected graphs with maximum clique size ω, the minimum value of the spectral radius of adjacency matrix is attained for a kite graph PKn−ω,ω , which consists of a complete graph Kω to a vertex of which a path Pn−ω is attached. For any fixed ω, a small interval to which the spectral radii of kites PKm,ω , m ≥ 1, belong is exhibited.
متن کاملEla the Minimum Spectral Radius of Graphs with a given Clique Number∗
In this paper, it is shown that among connected graphs with maximum clique size ω, the minimum value of the spectral radius of adjacency matrix is attained for a kite graph PKn−ω,ω , which consists of a complete graph Kω to a vertex of which a path Pn−ω is attached. For any fixed ω, a small interval to which the spectral radii of kites PKm,ω , m ≥ 1, belong is exhibited.
متن کاملOn Independent Domination Number of Graphs with given Minimum Degree
We prove a new upper bound on the independent domination number of graphs in terms of the number of vertices and the minimum degree. This bound is slightly better than that by J. Haviland 3] and settles Case = 2 of the corresponding conjecture by O. Favaron 2].
متن کاملThe Laplacian spectral radius of graphs with given matching number
In this paper, we show that of all graphs of order n with matching number β, the graphs with maximal spectral radius are Kn if n = 2β or 2β + 1; K2β+1 ∪Kn−2β−1 if 2β + 2 n < 3β + 2; Kβ ∨ Kn−β or K2β+1 ∪Kn−2β−1 if n = 3β + 2; Kβ ∨ Kn−β if n > 3β + 2, where Kt is the empty graph on t vertices. © 2006 Elsevier Inc. All rights reserved. AMS classification: 05C35; 05C50
متن کاملThe minimal spectral radius of graphs with a given diameter
The spectral radius of a graph (i.e., the largest eigenvalue of its corresponding adjacency matrix) plays an important role in modeling virus propagation in networks. In fact, the smaller the spectral radius, the larger the robustness of a network against the spread of viruses. Among all connected graphs on n nodes the pathPn has minimal spectral radius. However, its diameter D, i.e., the maxim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2023
ISSN: ['1873-1856', '0024-3795']
DOI: https://doi.org/10.1016/j.laa.2023.04.029