scholarly journals On the spectral radius of cactuses with perfect matchings

2011 ◽  
Vol 5 (1) ◽  
pp. 14-21 ◽  
Author(s):  
Ziwen Huang ◽  
Hanyuan Deng ◽  
Slobodan Simic
Keyword(s):  
Spectral Radius ◽  
Perfect Matchings ◽  
Unique Graph

Let C(2m, k) be the set of all cactuses on 2m vertices, k cycles, and with perfect matchings. In this paper, we identify in C(2m, k) the unique graph with the largest spectral radius.

scholarly journals On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jing-Ming Zhang ◽  
Ting-Zhu Huang ◽  
Ji-Ming Guo
Keyword(s):  
Spectral Radius ◽  
Perfect Matchings ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Bicyclic Graphs

The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.

SPECTRAL RADII OF UNICYCLIC GRAPHS WITH FIXED NUMBER OF CUT VERTICES

2011 ◽  
Vol 03 (02) ◽  
pp. 139-145 ◽  
Author(s):  
YI-ZHENG FAN ◽  
JING-MEI ZHANG ◽  
YI WANG
Keyword(s):  
Spectral Radius ◽  
Fixed Number ◽  
Unicyclic Graphs ◽  
Unique Graph

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.

The number of maximal cliques and spectral radius of graphs with certain forbidden subgraphs

2018 ◽  
Vol 10 (06) ◽  
pp. 1850071
Author(s):  
Ya-Lei Jin ◽  
Xiao-Dong Zhang
Keyword(s):  
Spectral Radius ◽  
Forbidden Subgraphs ◽  
Unique Graph ◽  
Turán Theorem ◽  
Turán Graph

Turán theorem states that the Turán graph [Formula: see text] is the unique graph which has the maximum edge number among the [Formula: see text]-free graphs of order [Formula: see text]. In this paper, we prove that [Formula: see text] has both the maximum number of maximal cliques and the maximum spectral radius among all graphs of order [Formula: see text] with [Formula: see text] and [Formula: see text], where [Formula: see text] stands for the maximum number of disjoint [Formula: see text]cliques of [Formula: see text].

A NOTE ON THE DISTANCE SPECTRAL RADIUS OF SOME GRAPHS

2014 ◽  
Vol 06 (01) ◽  
pp. 1450015 ◽  
Author(s):  
MILAN NATH ◽  
SOMNATH PAUL
Keyword(s):  
Spectral Radius ◽  
Minimum Degree ◽  
Clique Number ◽  
Minimal Distance ◽  
Vertex Connectivity ◽  
Unique Graph

We characterize graphs with minimal distance spectral radius in two classes of graphs: with vertex connectivity k and minimum degree at least k, and with given number of blocks. Moreover, we determine the unique graph that maximizes the distance spectral radius among all graphs with given clique number.

scholarly journals The Signless Laplacian Spectral Radius of Unicyclic and Bicyclic Graphs with a Given Girth

10.37236/670 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Ke Li ◽  
Ligong Wang ◽  
Guopeng Zhao
Keyword(s):  
Spectral Radius ◽  
Upper Bound ◽  
Extremal Graph ◽  
Laplacian Spectral Radius ◽  
Unicyclic Graphs ◽  
Signless Laplacian Spectral Radius ◽  
Disjoint Cycles ◽  
Signless Laplacian ◽  
Unique Graph ◽  
Bicyclic Graphs

Let $\mathcal{U}(n,g)$ and $\mathcal{B}(n,g)$ be the set of unicyclic graphs and bicyclic graphs on $n$ vertices with girth $g$, respectively. Let $\mathcal{B}_{1}(n,g)$ be the subclass of $\mathcal{B}(n,g)$ consisting of all bicyclic graphs with two edge-disjoint cycles and $\mathcal{B}_{2}(n,g)=\mathcal{B}(n,g)\backslash\mathcal{B}_{1}(n,g)$. This paper determines the unique graph with the maximal signless Laplacian spectral radius among all graphs in $\mathcal{U}(n,g)$ and $\mathcal{B}(n,g)$, respectively. Furthermore, an upper bound of the signless Laplacian spectral radius and the extremal graph for $\mathcal{B}(n,g)$ are also given.

scholarly journals On graft transformations decreasing distance spectral radius of graphs

2021 ◽  
Author(s):  
Yanna Wang ◽  
Bo Zhou
Keyword(s):  
Spectral Radius ◽  
Connected Graph ◽  
Minimum Distance ◽  
Distance Matrix ◽  
Largest Eigenvalue ◽  
Unique Graph ◽  
The Largest Eigenvalue

The distance spectral radius of a connected graph  is the largest eigenvalue of its distance matrix. In this paper, we give several less restricted graft transformations that decrease the distance spectral radius, and determine the unique   graph   with   minimum   distance  spectral radius among homeomorphically irreducible unicylic graphs on $n\geq 6$ vertices, and the unique tree with minimum distance spectral radius among trees on $n$  vertices with given number of  vertices of degree two, respectively.

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