scholarly journals The chromatic equivalence classes of the complements of graphs with the minimum real roots of their adjoint polynomials greater than -4

2008 ◽  
Vol 308 (10) ◽  
pp. 1830-1836 ◽  
Author(s):  
Haicheng Ma ◽  
Haizhen Ren
Keyword(s):  
Equivalence Classes ◽  
Real Roots ◽  
Chromatic Equivalence

scholarly journals Chromatic equivalence classes of certain generalized polygon trees

1997 ◽  
Vol 172 (1-3) ◽  
pp. 103-114 ◽  
Author(s):  
Yee-Hock Peng ◽  
C.H.C. Little ◽  
K.L. Teo ◽  
H. Wang
Keyword(s):  
Equivalence Classes ◽  
Generalized Polygon ◽  
Chromatic Equivalence

scholarly journals Chromatic equivalence classes of certain cycles with edges

2001 ◽  
Vol 232 (1-3) ◽  
pp. 175-183 ◽  
Author(s):  
Behnaz Omoomi ◽  
Yee-Hock Peng
Keyword(s):  
Equivalence Classes ◽  
Chromatic Equivalence

scholarly journals Chromatic Classes of 2-Connected (n,n+4)-Graphs with Exactly Three Triangles and at Least Two Induced 4-Cycles

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
G. C. Lau ◽  
Y. H. Peng
Keyword(s):  
Chromatic Polynomial ◽  
Equivalence Classes ◽  
Chromatic Equivalence

For a graph G, let P(G,λ) be its chromatic polynomial. Two graphs G and H are chromatically equivalent, denoted G∼H, if P(G,λ)=P(H,λ). A graph G is chromatically unique if P(H,λ)=P(G,λ) implies that H≅G. In this paper, we determine all chromatic equivalence classes of 2-connected (n,n+4)-graphs with exactly three triangles and at least two induced 4-cycles. As a byproduct of these, we obtain various new families of χ-equivalent graphs and χ-unique graphs.

scholarly journals MET: a Java package for fast molecule equivalence testing

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Jördis-Ann Schüler ◽  
Steffen Rechner ◽  
Matthias Müller-Hannemann
Keyword(s):  
Chemical Properties ◽  
Graph Isomorphism ◽  
Isomorphism Problem ◽  
Equivalence Classes ◽  
Equivalence Testing ◽  
Equivalence Test ◽  
Graph Isomorphism Problem ◽  
2D Structure ◽  
Node Labels ◽  
Labelled Graphs

AbstractAn important task in cheminformatics is to test whether two molecules are equivalent with respect to their 2D structure. Mathematically, this amounts to solving the graph isomorphism problem for labelled graphs. In this paper, we present an approach which exploits chemical properties and the local neighbourhood of atoms to define highly distinctive node labels. These characteristic labels are the key for clever partitioning molecules into molecule equivalence classes and an effective equivalence test. Based on extensive computational experiments, we show that our algorithm is significantly faster than existing implementations within , and . We provide our Java implementation as an easy-to-use, open-source package (via GitHub) which is compatible with . It fully supports the distinction of different isotopes and molecules with radicals.

Parallel and Distributed Processability of Objects

1989 ◽  
Vol 12 (3) ◽  
pp. 317-356
Author(s):  
David C. Rine
Keyword(s):  
Software Engineering ◽  
Software Design ◽  
Equivalence Classes ◽  
Minimum Amount ◽  
Software Components ◽  
Limited Extent ◽  
Design Environment ◽  
Distributed Software

Partitioning and allocating of software components are two important parts of software design in distributed software engineering. This paper presents two general algorithms that can, to a limited extent, be used as tools to assist in partitioning software components represented as objects in a distributed software design environment. One algorithm produces a partition (equivalence classes) of the objects, and a second algorithm allows a minimum amount of redundancy. Only binary relationships of actions (use or non-use) are considered in this paper.

scholarly journals A dichotomy for bounded displacement equivalence of Delone sets

2021 ◽  
pp. 1-18
Author(s):  
YOTAM SMILANSKY ◽  
YAAR SOLOMON
Keyword(s):  
Compact Space ◽  
Equivalence Classes ◽  
Natural Topology ◽  
Fell Topology ◽  
Local Complexity ◽  
Substitution Tilings ◽  
Local Topology ◽  
Delone Sets

Abstract We prove that in every compact space of Delone sets in ${\mathbb {R}}^d$ , which is minimal with respect to the action by translations, either all Delone sets are uniformly spread or continuously many distinct bounded displacement equivalence classes are represented, none of which contains a lattice. The implied limits are taken with respect to the Chabauty–Fell topology, which is the natural topology on the space of closed subsets of ${\mathbb {R}}^d$ . This topology coincides with the standard local topology in the finite local complexity setting, and it follows that the dichotomy holds for all minimal spaces of Delone sets associated with well-studied constructions such as cut-and-project sets and substitution tilings, whether or not finite local complexity is assumed.

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