On the distance spectral radius of unicyclic graphs with perfect matchings

2014 ◽  
Vol 27 ◽  
Author(s):  
Xiao Zhang
Keyword(s):  
Spectral Radius ◽  
Perfect Matchings ◽  
Unicyclic Graphs

Distance spectral radius of unicyclic graphs with fixed maximum degree

2019 ◽  
Vol 19 (04) ◽  
pp. 2050068
Author(s):  
Hezan Huang ◽  
Bo Zhou
Keyword(s):  
Spectral Radius ◽  
Connected Graph ◽  
Maximum Degree ◽  
Distance Matrix ◽  
The Other ◽  
Connected Graphs ◽  
Largest Eigenvalue ◽  
Unicyclic Graphs ◽  
The Largest Eigenvalue

The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. For integers [Formula: see text] and [Formula: see text] with [Formula: see text], we prove that among the connected graphs on [Formula: see text] vertices of given maximum degree [Formula: see text] with at least one cycle, the graph [Formula: see text] uniquely maximizes the distance spectral radius, where [Formula: see text] is the graph obtained from the disjoint star on [Formula: see text] vertices and path on [Formula: see text] vertices by adding two edges, one connecting the star center with a path end, and the other being a chord of the star.

On the edge-Szeged index of unicyclic graphs with perfect matchings

2020 ◽  
Vol 284 ◽  
pp. 207-223
Author(s):  
Shengjie He ◽  
Rong-Xia Hao ◽  
Yan-Quan Feng
Keyword(s):  
Perfect Matchings ◽  
Unicyclic Graphs ◽  
Szeged Index

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 The Laplacian Spectral Radius of a Class of Unicyclic Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Haixia Zhang
Keyword(s):  
Spectral Radius ◽  
Cycle Length ◽  
Laplacian Spectral Radius ◽  
Unicyclic Graphs

LetC(n,k)be the set of all unicyclic graphs withnvertices and cycle lengthk. For anyU∈C(n,k),Uconsists of the (unique) cycle (sayCk) of lengthkand a certain number of trees attached to the vertices ofCkhaving (in total)n-kedges. If there are at most two trees attached to the vertices ofCk, wherekis even, we identify in the class of unicyclic graphs those graphs whose Laplacian spectral radii are minimal.

Minimum Szeged index among unicyclic graphs with perfect matchings

2019 ◽  
Vol 38 (2) ◽  
pp. 443-455 ◽  
Author(s):  
Hechao Liu ◽  
Hanyuan Deng ◽  
Zikai Tang
Keyword(s):  
Perfect Matchings ◽  
Unicyclic Graphs ◽  
Szeged Index

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.

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