Sharp bounds on the distance spectral radius and the distance energy of graphs
نویسندگان
چکیده
منابع مشابه
Sharp Bounds on the PI Spectral Radius
In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.
متن کاملOn Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs
Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...
متن کاملsharp bounds on the pi spectral radius
in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.
متن کاملSome Sharp Upper Bounds on the Spectral Radius of Graphs
In this paper, we first give a relation between the adjacency spectral radius and the Q-spectral radius of a graph. Then using this result, we further give some new sharp upper bounds on the adjacency spectral radius of a graph in terms of degrees and the average 2-degrees of vertices. Some known results are also obtained.
متن کاملSharp Bounds on the Spectral Radius and the Energy of Graphs
Abstract Let G = (V,E) be a simple graph of order n with V (G) = {v1, v2, . . . , vn} and degree sequence d1, d2, . . . , dn. Let ρ(G) be the largest eigenvalue of adjacency matrix of G, and let E(G) be the energy of G. Denote (t)i = ∑ i∼j d α j and (m)i = (t)i/di , where α is a real number. In this paper, we obtain two sharp bounds on ρ(G) in terms of (m)i or (t)i, respectively. Also, we prese...
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: 2009
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.07.005