Results 101 to 110 of about 7,067 (209)

Bounds on the complex zeros of (Di)Chromatic polynomials and Potts-model partition functions

, 2001
We show that there exist universal constants C(r) such that, for all loopless graphs G of maximum degree less than or equal to r, the zeros (real or complex) of the chromatic polynomial P-G(q) lie in the disc \q\ 7.963907r.
Sokal, AD
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Graph polynomials and statistical physics [PDF]

, 2007
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.Includes bibliographical references (p. 53-54).We present several graph polynomials, of which the most important one is the Tutte polynomial.
Kim, Jae Ill, S.M. Massachusetts Institute of Technology
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Relationships between graph polynomials

, 2005
In this thesis, possible relationships between various graph polynomials are explored. Following pertinent denitions and results in algebra and graph theory, the polyno- mials are introduced. The denitions and computation of the chromatic polynomial, the
Gardner, Katie Maureen
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Graph Polynomials: Towards a Comparative Theory (Dagstuhl Seminar 16241)

, 2016
This report documents the program and the outcomes of Dagstuhl Seminar 16241 "Graph Polynomials: Towards a Comparative Theory". The area of graph polynomials has become in recent years incredibly active, with new applications and new graph ...
Ellis-Monaghan, Jo, Moffatt, Iain, Goodall, Andrew, Makowsky, Johann A.   +3 more
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Bounds on separated pairs of subgraphs, eigenvalues and related polynomials

We give a bound on the sizes of two sets of vertices at a given minimum distance (a separated pair of subgraphs) in a graph in terms of polynomials and the spectrum of the graph. We find properties of the polynomial optimizing the bound.
Dam, E.R. van
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Identifying regions in wide-angle scattering via graph-theoretical approaches

Journal of High Energy Physics
The method of regions, which provides a systematic approach for computing Feynman integrals involving multiple kinematic scales, proposes that a Feynman integral can be approximated and even reproduced by summing over integrals expanded in certain ...
Yao Ma
doaj   +1 more source

Factoring a Graph in Polynomial Time

European Journal of Combinatorics, 1987
The Cartesian product \(G\times H\) of graphs G and H has vertices (g,h) where g is a vertex in G and h a vertex in H. Two vertices of \(G\times H\), say \((g_ 1,h_ 1)\) and \((g_ 2,h_ 2)\), are connected by an edge in \(G\times H\), just when either \(\{g_ 1,g_ 2\}\) is an edge of G and \(h_ 1=h_ 2\), or when \(g_ 1=g_ 2\) and \(\{h_ 1,h_ 2\}\) is an ...
openaire   +1 more source

An Investigation on Graph Polynomials

, 2015
The chromatic polynomial of a graph , denoted π (, ), is the polynomial whose evaluations at positive integers count the number of (proper) -colourings of . This polynomial was introduced by Birkhoff in 1912 in an attempt to prove the famous Four Colour
Erey, Aysel
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Graph polynomials and their representations

, 2012
Graph polynomials are polynomials associated to graphs that encode the number of subgraphs with given properties. We list different frameworks used to define graph polynomials in the literature.
Trinks, Martin
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Reconstructing subgraph-counting graph polynomials of increasing families of graphs

, 2005
A graph polynomial P(G,x) is called reconstructible if it is uniquely determined by the polynomials of the vertex-deleted subgraphs of G for every graph G with at least three vertices.
Imrich, Wilfried, Sandi Klavžar, Klavžar, Sandi, Boštjan Brešar, Brešar, Boštjan, Wilfried Imrich   +5 more
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