product graphs
Recently Published Documents


TOTAL DOCUMENTS

383
(FIVE YEARS 123)

H-INDEX

18
(FIVE YEARS 4)

2021 ◽  
Vol 2132 (1) ◽  
pp. 012033
Author(s):  
Bo Zhu ◽  
Shumin Zhang ◽  
Chenfu Ye

Abstract The fractional strong matching preclusion number of a graph is the minimum number of edges and vertices whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the fractional strong matching preclusion number for the Cartesian product of a graph and a cycle. As an application, the fractional strong matching preclusion number for torus networks is also obtained.


2021 ◽  
Vol 410 ◽  
pp. 126438
Author(s):  
Sheyda Maddah ◽  
Modjtaba Ghorbani ◽  
Matthias Dehmer

Author(s):  
Jia-Bao Liu ◽  
Jiao-Jiao Gu ◽  
Sakander Hayat

Author(s):  
Suguru Hiranuma ◽  
Gen Kawatani ◽  
Naoki Matsumoto

The domatic number [Formula: see text] of a graph [Formula: see text] is the maximum number of disjoint dominating sets in a dominating set partition of a graph [Formula: see text]. For any graph [Formula: see text], [Formula: see text] where [Formula: see text] is the minimum degree of [Formula: see text], and [Formula: see text] is domatically full if the equality holds, i.e., [Formula: see text]. In this paper, we characterize domatically full Cartesian products of a path of order 2 and a tree of order at least 3. Moreover, we show a characterization of the Cartesian product of a longer path and a tree of order at least 3. By using these results, we also show that for any two trees of order at least 3, the Cartesian product of them is domatically full.


2021 ◽  
Vol 408 ◽  
pp. 126219
Author(s):  
Fengxia Liu ◽  
Xirinay Nurmamat ◽  
Panpan Zhang
Keyword(s):  

2021 ◽  
Author(s):  
Esther Heid ◽  
William H. Green

The estimation of chemical reaction properties such as activation energies, rates or yields is a central topic of computational chemistry. In contrast to molecular properties, where machine learning approaches such as graph convolutional neural networks (GCNNs) have excelled for a wide variety of tasks, no general and transferable adaptations of GCNNs for reactions have been developed yet. We therefore combined a popular cheminformatics reaction representation, the so-called condensed graph of reaction (CGR), with a recent GCNN architecture to arrive at a versatile, robust and compact deep learning model. The CGR is a superposition of the reactant and product graphs of a chemical reaction, and thus an ideal input for graph-based machine learning approaches. The model learns to create a data-driven, task dependent reaction embedding that does not rely on expert knowledge, similar to current molecular GCNNs. Our approach outperforms current state-of-the-art models in accuracy, is applicable even to imbalanced reactions and possesses excellent predictive capabilities for diverse target properties, such as activation energies, reaction enthalpies, rate constants, yields or reaction classes. We furthermore curated a large set of atom-mapped reactions along with their target properties, which can serve as benchmark datasets for future work. All datasets and the developed reaction GCNN model are available online, free of charge and open-source.


Author(s):  
Matthew Johnson ◽  
Daniël Paulusma ◽  
Erik Jan van Leeuwen

Let [Formula: see text] be an integer. From a set of [Formula: see text]-dimensional vectors, we obtain a [Formula: see text]-dot by letting each vector [Formula: see text] correspond to a vertex [Formula: see text] and by adding an edge between two vertices [Formula: see text] and [Formula: see text] if and only if their dot product [Formula: see text], for some fixed, positive threshold [Formula: see text]. Dot product graphs can be used to model social networks. Recognizing a [Formula: see text]-dot product graph is known to be NP -hard for all fixed [Formula: see text]. To understand the position of [Formula: see text]-dot product graphs in the landscape of graph classes, we consider the case [Formula: see text], and investigate how [Formula: see text]-dot product graphs relate to a number of other known graph classes including a number of well-known classes of intersection graphs.


Sign in / Sign up

Export Citation Format

Share Document