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    On the spectral radius of graphs with k-vertex cut.
    Ars Combinatoria (2008)
    Guoping WangQiongxiang HuangJing Cai
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    Keywords:
    Spectral Radius
    Topics:
    Graph theory and applications
    Advanced Graph Theory Research
    Graph Labeling and Dimension Problems
    SPECTRAL RADII OF UNICYCLIC GRAPHS WITH FIXED NUMBER OF CUT VERTICES
    Discrete Mathematics Algorithms and Applications (2011)
    Yi-Zheng FanJingmei ZhangYi Wang
    Let [Formula: see text] be the set of unicyclic graphs with n vertices and k cut vertices. In this paper, we determine the unique graph with the maximal spectral radius among all graphs in [Formula: see text] for 1 ≤ k ≤ n - 3.
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    Metric Dimension
    Citations (3)
    On the spectral radius of graphs without a star forest
    Discrete Mathematics (2021)
    Mingzhu ChenA-Ming LiuXiao‐Dong Zhang
    Spectral Radius
    Adjacency matrix
    Cayley graph
    Disjoint sets
    Star (game theory)
    Disjoint union (topology)
    Cograph
    Citations (25)
    Distance spectral radius of digraphs with given connectivity
    Discrete Mathematics (2012)
    Huiqiu LinWeihua YangHailiang ZhangJinlong Shu
    Spectral Radius
    Digraph
    Distance matrix
    Connectivity
    Minimum distance
    Citations (25)
    Ordering Graphs with Cut Edges by Their Spectral Radii
    应用数学学报(英文版) (2012)
    Fang Faculty
    Let Gnk denote a set of graphs with n vertices and k cut edges. In this paper, we obtain an order of the first four graphs in Gnk in terms of their spectral radii for 6 ≤ k ≤ (n-2)/3.
    Clique-sum
    Citations (0)
    Maximum Spectral Radius of Graphs with Connectivity at Most k and Minimum Degree at Least δ
    Lecture notes in computer science (2013)
    Hongliang LuYuqing Lin
    Spectral Radius
    Degree (music)
    Citations (0)
    On the generalized distance spectral radius of graphs
    arXiv (Cornell University) (2019)
    Shu‐Yu CuiGui‐Xian TianLu Zheng
    The generalized distance spectral radius of a connected graph $G$ is the spectral radius of the generalized distance matrix of $G$, defined by $$D_α(G)=αTr(G)+(1-α)D(G), \;\;0\leα\le 1,$$ where $D(G)$ and $Tr(G)$ denote the distance matrix and diagonal matrix of the vertex transmissions of $G$, respectively. This paper characterizes the unique graph with minimum generalized distance spectral radius among the connected graphs with fixed chromatic number, which answers a question about the generalized distance spectral radius in spectral extremal theories. In addition, we also determine graphs with minimum generalized distance spectral radius among the $n$-vertex trees and unicyclic graphs, respectively. These results generalize some known results about distance spectral radius and distance signless Laplacian spectral radius of graphs.
    Spectral Radius
    Distance matrix
    Resistance Distance
    Connectivity
    Citations (5)
    On the spectral radius of graphs with cut edges
    Linear Algebra and its Applications (2004)
    Huiqing LiuMei LuFeng Tian
    Spectral Radius
    Citations (71)
    Bipartite Graphs with the First and Second Largest Laplacian Spectral Radius
    东华大学学报(英文版) (2011)
    Aiping Deng
    Let kn be the class of bipartite graphs with n vertices and k cut edges.The extremal graphs with the first and the second largest Laplacian spectral radius among all graphs in kn are presented.The bounds of the Laplacian spectral radius of these extremal graphs are also obtained.
    Spectral Radius
    Indifference graph
    Citations (0)
    Lower bounds of distance Laplacian spectral radii of n-vertex graphs in terms of matching number
    Linear Algebra and its Applications (2016)
    Fenglei TianDein WongXiaobin Ma
    Spectral Radius
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    The signless Laplacian spectral radius of graphs with given number of cut vertices
    Discussiones Mathematicae Graph Theory (2010)
    Cui LinYi-Zheng Fan
    Spectral Radius
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