Results 81 to 90 of about 7,067 (209)

Discovering factors of graph polynomials [PDF]

, 2019
One of the most common approaches in studying any polynomial is by looking at its factors. Over the years, different graph polynomials have been defined for both undirected and directed graphs, including the Tutte polynomial, chromatic polynomial ...
Nur Syazwani binti Sjafrial
core   +1 more source

Chromatic Polynomials of Oriented Graphs

The Electronic Journal of Combinatorics, 2019
The oriented chromatic polynomial of a oriented graph outputs the number of oriented $k$-colourings for any input $k$. We fully classify those oriented graphs for which the oriented graph has the same chromatic polynomial as the underlying simple graph, closing an open problem posed by Sopena.
Danielle Cox, Christopher Duffy 0001
openaire   +4 more sources

New expressions for order polynomials and chromatic polynomials

, 2019
Let =(,) be a simple graph with ={1,2,…,} and (,) be its chromatic polynomial. For an ordering =(1,2,…,) of elements of , let () be the number of integers , where 1≤≤−1 , with either
Dong, F. M.
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Zagreb Polynomials of Three Graph Operators

, 2016
22nd International Conference on Finite and Infinite Dimensional Complex Analysis and Applications (ICFIDCAA) -- AUG 08-11, 2014 -- Dongguk Univ, Gyeongju, SOUTH KOREAIn general, the relations among Zagreb polynomials on three graph operators are ...
Cevik, A. Sinan, Lokesha, V., Cangul, I. Naci, Bindusree, A. R.   +3 more
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Tutte polynomials for directed graphs

Journal of Combinatorial Theory, Series B, 2020
The Tutte polynomial is a fundamental invariant of graphs. In this article, we define and study a generalization of the Tutte polynomial for directed graphs, that we name B-polynomial. The B-polynomial has three variables, but when specialized to the case of graphs (that is, digraphs where arcs come in pairs with opposite directions), one of the ...
Jordan Awan, Olivier Bernardi
openaire   +4 more sources

The Hosoya Entropy of a Graph

Entropy, 2015
This paper demonstrates properties of Hosoya entropy, a quantitative measure of graph complexity based on a decomposition of the vertices linked to partial Hosoya polynomials.
Abbe Mowshowitz, Matthias Dehmer
doaj   +1 more source

Chromatic roots are dense in the whole complex plane

, 2004
I show that the zeros of the chromatic polynomials P-G(q) for the generalized theta graphs Theta((s.p)) are taken together, dense in the whole complex plane with the possible exception of the disc \q - l\ < l.
Sokal, AD
core  

Zeros of Jones Polynomials of Graphs

The Electronic Journal of Combinatorics, 2015
In this paper, we introduce the Jones polynomial of a graph $G=(V,E)$ with $k$  components as the following specialization of the Tutte polynomial:$$J_G(t)=(-1)^{|V|-k}t^{|E|-|V|+k}T_G(-t,-t^{-1}).$$We first study its basic properties and determine certain extreme coefficients.
Fengming Dong, Xian'an Jin
openaire   +2 more sources

Tutte Polynomials and Graph Symmetries

, 2022
The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic and the flow polynomials. This two-variable polynomial with integral coefficients is known to carry important information about the properties of the graph.
Noura Alderai, Nafaa Chbili, Roba Ali, Raghd AlQedra   +3 more
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Applications of magnesium iodide structure via modified-polynomials

Scientific Reports
A relatively recent approach in molecular graph theory for analyzing chemical networks and structures is called a modified polynomial. It emphasizes the characteristics of molecules through the use of a polynomial-based procedure and presents numerical ...
Haleemah Ghazwani, Muhammad Kamran Jamil, Ali Ahmad, Muhammad Azeem, Ali N. A. Koam   +4 more
doaj   +1 more source