scholarly journals Upper bounds for the signless Laplacian spectral radius of graphs on surfaces

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3473-3481
Author(s):  
Xiaodan Chen ◽  
Yaoping Hou
Keyword(s):  
Spectral Radius ◽  
Upper Bounds ◽  
Outerplanar Graphs ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Graphs On Surfaces ◽  
Halin Graphs

In this paper, we present some new upper bounds for the signless Laplacian spectral radius of graphs embeddable on a fixed surface, which improve several previously known results. We also give several improved upper bounds for the signless Laplacian spectral radius of outerplanar graphs and Halin graphs.

scholarly journals The signless Laplacian spectral radius of bounded degree graphs on surfaces

2015 ◽  
Vol 9 (2) ◽  
pp. 332-346 ◽  
Author(s):  
Guihai Yu ◽  
Lihua Feng ◽  
Aleksandar Ilic ◽  
Dragan Stevanovic
Keyword(s):  
Spectral Radius ◽  
Simple Graph ◽  
Extremal Graphs ◽  
Outerplanar Graphs ◽  
Bounded Degree ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Graphs On Surfaces ◽  
Better Than

Let G be an n-vertex (n ? 3) simple graph embeddable on a surface of Euler genus (the number of crosscaps plus twice the number of handles). In this paper, we present upper bounds for the signless Laplacian spectral radius of planar graphs, outerplanar graphs and Halin graphs, respectively, in terms of order and maximum degree. We also demonstrate that our bounds are sometimes better than known ones. For outerplanar graphs without internal triangles, we determine the extremal graphs with the maximum and minimum signless Laplacian spectral radii.

TWO SHARP UPPER BOUNDS FOR THE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF GRAPHS

2011 ◽  
Vol 03 (02) ◽  
pp. 185-191 ◽  
Author(s):  
YA-HONG CHEN ◽  
RONG-YING PAN ◽  
XIAO-DONG ZHANG
Keyword(s):  
Spectral Radius ◽  
Upper Bound ◽  
Adjacency Matrix ◽  
Laplacian Matrix ◽  
Upper Bounds ◽  
Extremal Graphs ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Matrix ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian

The signless Laplacian matrix of a graph is the sum of its degree diagonal and adjacency matrices. In this paper, we present a sharp upper bound for the spectral radius of the adjacency matrix of a graph. Then this result and other known results are used to obtain two new sharp upper bounds for the signless Laplacian spectral radius. Moreover, the extremal graphs which attain an upper bound are characterized.

On spectra and spectral radius of Signless Laplacian of power graphs of some finite groups

2020 ◽  
pp. 2150090
Author(s):  
Subarsha Banerjee ◽  
Avishek Adhikari
Keyword(s):  
Spectral Radius ◽  
Finite Groups ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Laplacian Spectral Radius ◽  
Power Graph ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Extremal Values ◽  
A Finite Group

Let [Formula: see text] denote the power graph of a finite group [Formula: see text]. Let [Formula: see text] denote the Signless Laplacian spectral radius of [Formula: see text]. In this paper, we give lower and upper bounds on [Formula: see text] for any [Formula: see text] and find those graphs for which the extremal values are attained. We give a comparison between the bounds obtained and exact value of [Formula: see text] for any [Formula: see text]. We then find the eigenvalues of [Formula: see text] and give lower and upper bounds on the spectral radius of [Formula: see text]. When [Formula: see text] and [Formula: see text] where [Formula: see text] are primes and [Formula: see text] is a positive integer, we obtain sharper bounds on [Formula: see text]. Finally, we make a conjecture on [Formula: see text] for any [Formula: see text].

scholarly journals Upper bounds on Q-spectral radius of book-free and/or $K_{s,t}$-free graphs

2017 ◽  
Vol 32 ◽  
pp. 447-453
Author(s):  
Qi Kong ◽  
Ligong Wang
Keyword(s):  
Spectral Radius ◽  
Regular Graph ◽  
Maximum Degree ◽  
Strongly Regular Graph ◽  
Upper Bounds ◽  
Free Graph ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Strongly Regular

In this paper, we prove two results about the signless Laplacian spectral radius $q(G)$ of a graph $G$ of order $n$ with maximum degree $\Delta$. Let $B_{n}=K_{2}+\overline{K_{n}}$ denote a book, i.e., the graph $B_{n}$ consists of $n$ triangles sharing an edge. The results are the following: (1) Let $1< k\leq l< \Delta < n$ and $G$ be a connected \{$B_{k+1},K_{2,l+1}$\}-free graph of order $n$ with maximum degree $\Delta$. Then $$\displaystyle q(G)\leq \frac{1}{4}[3\Delta+k-2l+1+\sqrt{(3\Delta+k-2l+1)^{2}+16l(\Delta+n-1)}$$ with equality if and only if $G$ is a strongly regular graph with parameters ($\Delta$, $k$, $l$). (2) Let $s\geq t\geq 3$, and let $G$ be a connected $K_{s,t}$-free graph of order $n$ $(n\geq s+t)$. Then $$q(G)\leq n+(s-t+1)^{1/t}n^{1-1/t}+(t-1)(n-1)^{1-3/t}+t-3.$$

Bounds for the skew Laplacian spectral radius of oriented graphs

2019 ◽  
Vol 35 (1) ◽  
pp. 31-40 ◽  
Author(s):  
BILAL A. CHAT ◽  
◽  
HILAL A. GANIE ◽  
S. PIRZADA ◽  
◽  
...  
Keyword(s):  
Spectral Radius ◽  
Upper Bound ◽  
Laplacian Matrix ◽  
Upper Bounds ◽  
Extremal Graphs ◽  
Arbitrary Direction ◽  
Laplacian Spectral Radius ◽  
Underlying Graph ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian

We consider the skew Laplacian matrix of a digraph −→G obtained by giving an arbitrary direction to the edges of a graph G having n vertices and m edges. We obtain an upper bound for the skew Laplacian spectral radius in terms of the adjacency and the signless Laplacian spectral radius of the underlying graph G. We also obtain upper bounds for the skew Laplacian spectral radius and skew spectral radius, in terms of various parameters associated with the structure of the digraph −→G and characterize the extremal graphs.

SPECTRAL RADIUS AND AVERAGE 2-DEGREE SEQUENCE OF A GRAPH

2014 ◽  
Vol 06 (02) ◽  
pp. 1450029 ◽  
Author(s):  
YU-PEI HUANG ◽  
CHIH-WEN WENG
Keyword(s):  
Spectral Radius ◽  
Maximum Degree ◽  
Degree Sequence ◽  
Discrete Math ◽  
Upper Bounds ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Degree Of A Vertex ◽  
Signless Laplacian ◽  
Simple Connected Graph

In a simple connected graph, the average 2-degree of a vertex is the average degree of its neighbors. With the average 2-degree sequence and the maximum degree ratio of adjacent vertices, we present a sharp upper bound of the spectral radius of the adjacency matrix of a graph, which improves a result in [Y. H. Chen, R. Y. Pan and X. D. Zhang, Two sharp upper bounds for the signless Laplacian spectral radius of graphs, Discrete Math. Algorithms Appl.3(2) (2011) 185–191].

The signless Laplacian spectral radius of graphs on surfaces

2013 ◽  
Vol 61 (5) ◽  
pp. 573-581 ◽  
Author(s):  
Lihua Feng ◽  
Guihai Yu ◽  
Aleksandar Ilić ◽  
Dragan Stevanović
Keyword(s):  
Spectral Radius ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Graphs On Surfaces
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