scholarly journals Maximal distance spectral radius of 4-chromatic planar graphs

2021 ◽  
Vol 618 ◽  
pp. 183-202
Author(s):  
Aysel Erey
Keyword(s):  
Spectral Radius ◽  
Planar Graphs ◽  
Maximal Distance

scholarly journals A note on distance spectral radius of trees

2017 ◽  
Vol 5 (1) ◽  
pp. 296-300
Author(s):  
Yanna Wang ◽  
Rundan Xing ◽  
Bo Zhou ◽  
Fengming Dong
Keyword(s):  
Spectral Radius ◽  
Connected Graph ◽  
Distance Matrix ◽  
Largest Eigenvalue ◽  
Maximal Distance ◽  
The Largest Eigenvalue

Abstract The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. We determine the unique non-starlike non-caterpillar tree with maximal distance spectral radius.

scholarly journals On the maximal distance spectral radius of graphs without a pendent vertex

2013 ◽  
Vol 438 (11) ◽  
pp. 4260-4278 ◽  
Author(s):  
Surya Sekhar Bose ◽  
Milan Nath ◽  
Somnath Paul
Keyword(s):  
Spectral Radius ◽  
Maximal Distance ◽  
Pendent Vertex

GRAPH TRANSFORMATION AND DISTANCE SPECTRAL RADIUS

2013 ◽  
Vol 05 (03) ◽  
pp. 1350014
Author(s):  
MILAN NATH ◽  
SOMNATH PAUL
Keyword(s):  
Spectral Radius ◽  
Special Class ◽  
Maximum Degree ◽  
Graph Transformation ◽  
Underlying Structure ◽  
Minimal Distance ◽  
Maximal Distance

Trees are very common in the theory and applications of combinatorics. In this paper, we consider graphs whose underlying structure is a tree and study the behavior of the distance spectral radius under a graph transformation. As an application, we find the corona tree that maximizes the distance spectral radius among all corona trees with a fixed maximum degree. We also find the graph with minimal (maximal) distance spectral radius among all corona trees. Finally, we determine the graph with minimal distance spectral radius in a special class of corona trees.

scholarly journals On Maximal Distance Energy

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 360
Author(s):  
Shaowei Sun ◽  
Kinkar Chandra Das ◽  
Yilun Shang
Keyword(s):  
Spectral Radius ◽  
Linear Algebra ◽  
Special Class ◽  
Distance Matrix ◽  
Maximum Distance ◽  
Connected Subgraph ◽  
Cut Vertex ◽  
Maximal Distance ◽  
Clique Trees ◽  
Clique Tree

Let G be a graph of order n. If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy ED(G) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D(G). In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39.

Maximal distance spectral radius of trees

2019 ◽  
Vol 11 (02) ◽  
pp. 1950025
Author(s):  
S. S. Bose ◽  
M. Nath ◽  
D. Sarma
Keyword(s):  
Spectral Radius ◽  
Maximal Distance ◽  
Pendent Vertex

In this paper, we determine the unique tree that maximizes the distance spectral radius in the class of all trees in which each non-pendent vertex has degree at least [Formula: see text].

scholarly journals Maxima of the signless Laplacian spectral radius for planar graphs

2015 ◽  
Vol 30 ◽  
pp. 795-811 ◽  
Author(s):  
Guanglong Yu ◽  
Jianyong Wong ◽  
Shu-guang Guo
Keyword(s):  
Spectral Radius ◽  
Planar Graphs ◽  
Laplacian Spectral Radius ◽  
Largest Eigenvalue ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
The Largest Eigenvalue

The signless Laplacian spectral radius of a graph is the largest eigenvalue of its signless Laplacian. In this paper, we prove that the graph $K_{2}\nabla P_{n-2}$ has the maximal signless Laplacian spectral radius among all planar graphs of order $n\geq 456$.

ON THE MAXIMAL DISTANCE SPECTRAL RADIUS IN A CLASS OF BICYCLIC GRAPHS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250061 ◽  
Author(s):  
SOMNATH PAUL
Keyword(s):  
Spectral Radius ◽  
Disjoint Paths ◽  
Induced Subgraph ◽  
Connected Graphs ◽  
Maximal Distance ◽  
Bicyclic Graphs ◽  
Vertex Disjoint

Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. Let Pp+1 = x1x2⋯xp+1, Pt+1 = y1y2⋯yt+1 and Pq+1 = z1z2⋯zq+1 be three vertex-disjoint paths. Identifying the initial vertices as u0 and the terminal vertices as v0, the resultant graph, denoted by θ(p; t; q), is called a θ-graph. Let [Formula: see text] be the class of all bicyclic graphs on n vertices, which contain a θ-graph as an induced subgraph. In this paper, we study the distance spectral radius of bicyclic graphs in [Formula: see text], and determine the graph with the largest distance spectral radius.

Acute Constraints in Straight-Line Drawings of Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 994-1001
Author(s):  
Akane SETO ◽  
Aleksandar SHURBEVSKI ◽  
Hiroshi NAGAMOCHI ◽  
Peter EADES
Keyword(s):  
Planar Graphs ◽  
Line Drawings ◽  
Straight Line
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