scholarly journals Note on chromatic polynomials of the threshold graphs

2019 ◽  
Vol 7 (2) ◽  
pp. 217-224
Author(s):  
Noureddine Chikh ◽  
◽  
Miloud Mihoubi ◽  
Keyword(s):  
Chromatic Polynomials ◽  
Threshold Graphs

On 3-colorings of bipartitep-threshold graphs

1987 ◽  
Vol 11 (3) ◽  
pp. 327-338 ◽  
Author(s):  
Ioan Tomescu
Keyword(s):  
Threshold Graphs

scholarly journals Approximations for chromatic polynomials

1976 ◽  
Vol 20 (1) ◽  
pp. 5-19 ◽  
Author(s):  
N.L Biggs ◽  
G.H.J Meredith
Keyword(s):  
Chromatic Polynomials

scholarly journals A note on the eigenvalue free intervals of some classes of signed threshold graphs

2019 ◽  
Vol 7 (1) ◽  
pp. 218-225
Author(s):  
Milica Anđelić ◽  
Tamara Koledin ◽  
Zoran Stanić
Keyword(s):  
Tridiagonal Matrix ◽  
Constant Sign ◽  
Equitable Partition ◽  
Elementary Matrix ◽  
Matrix Operations ◽  
Threshold Graphs ◽  
The Matrix ◽  
Threshold Graph

Abstract We consider a particular class of signed threshold graphs and their eigenvalues. If Ġ is such a threshold graph and Q(Ġ ) is a quotient matrix that arises from the equitable partition of Ġ , then we use a sequence of elementary matrix operations to prove that the matrix Q(Ġ ) – xI (x ∈ ℝ) is row equivalent to a tridiagonal matrix whose determinant is, under certain conditions, of the constant sign. In this way we determine certain intervals in which Ġ has no eigenvalues.

ON THE PAIRWISE COMPATIBILITY PROPERTY OF SOME SUPERCLASSES OF THRESHOLD GRAPHS

2013 ◽  
Vol 05 (02) ◽  
pp. 1360002 ◽  
Author(s):  
TIZIANA CALAMONERI ◽  
ROSSELLA PETRESCHI ◽  
BLERINA SINAIMERI
Keyword(s):  
The Other ◽  
Real Numbers ◽  
Weighted Tree ◽  
Positive Edge ◽  
Threshold Graphs ◽  
Compatibility Graph ◽  
Unique Path ◽  
Compatibility Property

A graph G is called a pairwise compatibility graph (PCG) if there exists a positive edge weighted tree T and two non-negative real numbers d min and d max such that each leaf lu of T corresponds to a node u ∈ V and there is an edge (u, v) ∈ E if and only if d min ≤ dT (lu, lv) ≤ d max , where dT (lu, lv) is the sum of the weights of the edges on the unique path from lu to lv in T. In this paper we study the relations between the pairwise compatibility property and superclasses of threshold graphs, i.e., graphs where the neighborhoods of any couple of nodes either coincide or are included one into the other. Namely, we prove that some of these superclasses belong to the PCG class. Moreover, we tackle the problem of characterizing the class of graphs that are PCGs of a star, deducing that also these graphs are a generalization of threshold graphs.

scholarly journals On Weak Chromatic Polynomials of Mixed Graphs

2013 ◽  
Vol 31 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Matthias Beck ◽  
Daniel Blado ◽  
Joseph Crawford ◽  
Taïna Jean-Louis ◽  
Michael Young
Keyword(s):  
Chromatic Polynomials ◽  
Mixed Graphs

On Universal Threshold Graphs

1997 ◽  
pp. 375-392
Author(s):  
P.L. Hammer ◽  
A.K. Kelmans
Keyword(s):  
Threshold Graphs

Pathwidth and Searching in Parameterized Threshold Graphs

2010 ◽  
pp. 293-304 ◽  
Author(s):  
D. Sai Krishna ◽  
T. V. Thirumala Reddy ◽  
B. Sai Shashank ◽  
C. Pandu Rangan
Keyword(s):  
Threshold Graphs
Sign in / Sign up

Export Citation Format

Share Document