scholarly journals The Counting Polynomial of a Supersolvable Arrangement

1995 ◽  
Vol 116 (2) ◽  
pp. 356-364 ◽  
Author(s):  
L. Paris
Keyword(s):  
Supersolvable Arrangement ◽  
Counting Polynomial

scholarly journals Orbit Polynomial of Graphs versus Polynomial with Integer Coefficients

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 710
Author(s):  
Modjtaba Ghorbani ◽  
Maryam Jalali-Rad ◽  
Matthias Dehmer
Keyword(s):  
Integer Coefficients ◽  
Integer Polynomial ◽  
Counting Polynomial

Suppose ai indicates the number of orbits of size i in graph G. A new counting polynomial, namely an orbit polynomial, is defined as OG(x) = ∑i aixi. Its modified version is obtained by subtracting the orbit polynomial from 1. In the present paper, we studied the conditions under which an integer polynomial can arise as an orbit polynomial of a graph. Additionally, we surveyed graphs with a small number of orbits and characterized several classes of graphs with respect to their orbit polynomials.

scholarly journals Counting polynomial subset sums

2018 ◽  
Vol 47 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Jiyou Li ◽  
Daqing Wan
Keyword(s):  
Subset Sums ◽  
Counting Polynomial

About the cube polynomial of Extended Fibonacci Cubes

2018 ◽  
Vol 27 (1) ◽  
pp. 95-100
Author(s):  
Ioana Zelina ◽  
◽  
Mara Hajdu-Măcelaru ◽  
Cristina Ţicală ◽  
◽  
...  
Keyword(s):  
Distributed System ◽  
Network Topology ◽  
Counting Polynomial

The hypercube is one of the best model for the network topology of a distributed system. In this paper we determine the cube polynomial of Extended Fibonacci Cubes, which is the counting polynomial for the number of induced k-dimensional hypercubes in Extended Fibonacci Cubes.

scholarly journals Some Applications of Wagner's Weighted Subgraph Counting Polynomial

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Ferenc Bencs ◽  
Péter Csikvári ◽  
Guus Regts
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Line Graphs ◽  
Uniform Hypergraph ◽  
Edge Cover ◽  
Absolute Value ◽  
On Line ◽  
Ferromagnetic Ising Model ◽  
Cover Polynomial ◽  
Counting Polynomial

We use Wagner's weighted subgraph counting polynomial to prove that the partition function of the anti-ferromagnetic Ising model on line graphs is real rooted and to prove that roots of the edge cover polynomial have absolute value at most $4$. We more generally show that roots of the edge cover polynomial of a $k$-uniform hypergraph have absolute value at most $2^k$, and discuss applications of this to the roots of domination polynomials of graphs. We moreover discuss how our results relate to efficient algorithms for approximately computing evaluations of these polynomials.  

scholarly journals Supersolvable orders and inductively free arrangements

2017 ◽  
Vol 15 (1) ◽  
pp. 587-594
Author(s):  
Ruimei Gao ◽  
Xiupeng Cui ◽  
Zhe Li
Keyword(s):  
Free Arrangement ◽  
Supersolvable Arrangement

Abstract In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order. Our main results improve the conclusion that every supersolvable arrangement is inductively free. In addition, we assert that the inductively free arrangement with the required induction table is supersolvable.

On the z-counting polynomial for edge-weighted graphs

1992 ◽  
Vol 9 (4) ◽  
pp. 381-387 ◽  
Author(s):  
Sonja Nikolić ◽  
Dejan Plavšić ◽  
Nenad Trinajstić
Keyword(s):  
Weighted Graphs ◽  
Counting Polynomial

scholarly journals Hosoya-Diudea polynomial in hyper structures

2013 ◽  
Vol 21 (2) ◽  
pp. 83-92
Author(s):  
M. P. Vlad ◽  
M. V. Diudea
Keyword(s):  
Local Property ◽  
Matrix Operator ◽  
Icosahedral Symmetry ◽  
Polynomial Coefficients ◽  
Shell Matrix ◽  
Finite Sequences ◽  
Hosoya Polynomial ◽  
Counting Polynomial ◽  
Square Matrix

Abstract Hosoya polynomial counts finite sequences of distances in a graph G; more exactly, it counts the number of points/atoms lying at a given distance in G. The polynomial coefficients are calculable by means of layer/shell matrices. Shell matrix operator enables the transformation of any square matrix in the corresponding layer/shell matrix, thus generalizing the local property counting according to its distribution by the distances in G. This represents the “Hosoya-Diudea” generalized counting polynomial. We applied this theory to several hypothetical nanostructures with icosahedral symmetry.

Counting polynomial functions $(\mod p^n)$

1968 ◽  
Vol 35 (4) ◽  
pp. 835-838 ◽  
Author(s):  
Gordon Keller ◽  
F. R. Olson
Keyword(s):  
Polynomial Functions ◽  
Counting Polynomial ◽  
Mod P

Computing a Counting Polynomial of an Infinite Family of Linear Polycene Parallelogram Benzenoid Graph P(a,b)

2007 ◽  
Vol 3 (1) ◽  
pp. 186-190
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Infinite Family ◽  
Benzenoid Graph ◽  
First Derivative ◽  
Omega Polynomial ◽  
Counting Polynomial ◽  
First Time

Omega polynomial was defined by M.V. Diudea in 2006 as  where the number of edges co-distant with e is denoted by n(e). One can obtain Theta Θ, Sadhana Sd and Pi Π polynomials by replacing xn(e) with n(e)xn(e), x|E|-n(e) and n(e)x|E|-n(e) in Omega polynomial, respectively. Then Theta Θ, Sadhana Sd and Pi Π indices will be the first derivative of Θ(x), Sd(x) and Π(x) evaluated at x=1. In this paper, Pi Π(G,x) polynomial and Pi Π(G) index of an infinite family of linear polycene parallelogram benzenoid graph P(a,b) are computed for the first time.

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