scholarly journals Deciding the Bell Number for Hereditary Graph Properties

2016 ◽  
Vol 30 (2) ◽  
pp. 1015-1031 ◽  
Author(s):  
Aistis Atminas ◽  
Andrew Collins ◽  
Jan Foniok ◽  
Vadim V. Lozin
Keyword(s):  
Graph Properties ◽  
Bell Number

scholarly journals A jump to the bell number for hereditary graph properties

2005 ◽  
Vol 95 (1) ◽  
pp. 29-48 ◽  
Author(s):  
József Balogh ◽  
Béla Bollobás ◽  
David Weinreich
Keyword(s):  
Graph Properties ◽  
Bell Number

scholarly journals Deciding the Bell Number for Hereditary Graph Properties

2014 ◽  
pp. 69-80
Author(s):  
Aistis Atminas ◽  
Andrew Collins ◽  
Jan Foniok ◽  
Vadim V. Lozin
Keyword(s):  
Graph Properties ◽  
Bell Number

scholarly journals Complete and incomplete Bell polynomials associated with Lah–Bell numbers and polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Lee-Chae Jang ◽  
Hyunseok Lee ◽  
Han-Young Kim
Keyword(s):  
Bell Polynomials ◽  
Bell Numbers ◽  
Bell Number ◽  
Finite Sums

AbstractThe nth r-extended Lah–Bell number is defined as the number of ways a set with $n+r$ n + r elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to introduce incomplete r-extended Lah–Bell polynomials and complete r-extended Lah–Bell polynomials respectively as multivariate versions of r-Lah numbers and the r-extended Lah–Bell numbers and to investigate some properties and identities for these polynomials. From these investigations we obtain some expressions for the r-Lah numbers and the r-extended Lah–Bell numbers as finite sums.

You Only Traverse Twice: A YOTT Placement, Routing, and Timing Approach for CGRAs

2021 ◽  
Vol 20 (5s) ◽  
pp. 1-25
Author(s):  
Michael Canesche ◽  
Westerley Carvalho ◽  
Lucas Reis ◽  
Matheus Oliveira ◽  
Salles Magalhães ◽  
...  
Keyword(s):  
Execution Time ◽  
High Performance ◽  
Coarse Grained ◽  
Optimal Placement ◽  
Greedy Heuristics ◽  
High Quality ◽  
Solution Quality ◽  
Graph Traversal ◽  
Trade Offs ◽  
Graph Properties

Coarse-grained reconfigurable architecture (CGRA) mapping involves three main steps: placement, routing, and timing. The mapping is an NP-complete problem, and a common strategy is to decouple this process into its independent steps. This work focuses on the placement step, and its aim is to propose a technique that is both reasonably fast and leads to high-performance solutions. Furthermore, a near-optimal placement simplifies the following routing and timing steps. Exact solutions cannot find placements in a reasonable execution time as input designs increase in size. Heuristic solutions include meta-heuristics, such as Simulated Annealing (SA) and fast and straightforward greedy heuristics based on graph traversal. However, as these approaches are probabilistic and have a large design space, it is not easy to provide both run-time efficiency and good solution quality. We propose a graph traversal heuristic that provides the best of both: high-quality placements similar to SA and the execution time of graph traversal approaches. Our placement introduces novel ideas based on “you only traverse twice” (YOTT) approach that performs a two-step graph traversal. The first traversal generates annotated data to guide the second step, which greedily performs the placement, node per node, aided by the annotated data and target architecture constraints. We introduce three new concepts to implement this technique: I/O and reconvergence annotation, degree matching, and look-ahead placement. Our analysis of this approach explores the placement execution time/quality trade-offs. We point out insights on how to analyze graph properties during dataflow mapping. Our results show that YOTT is 60.6 , 9.7 , and 2.3 faster than a high-quality SA, bounding box SA VPR, and multi-single traversal placements, respectively. Furthermore, YOTT reduces the average wire length and the maximal FIFO size (additional timing requirement on CGRAs) to avoid delay mismatches in fully pipelined architectures.

THE CONJUGACY CLASSES OF SOME FINITE METABELIAN GROUPS AND THEIR RELATED GRAPHS

2016 ◽  
Vol 79 (1) ◽  
Author(s):  
Nor Haniza Sarmin ◽  
Ain Asyikin Ibrahim ◽  
Alia Husna Mohd Noor ◽  
Sanaa Mohamed Saleh Omer
Keyword(s):  
Graph Theory ◽  
Conjugacy Class ◽  
Dihedral Group ◽  
Clique Number ◽  
Conjugacy Classes ◽  
Quaternion Group ◽  
Metabelian Groups ◽  
Dominating Number ◽  
Graph Properties ◽  
Class Graph

In this paper, the conjugacy classes of three metabelian groups, namely the Quasi-dihedral group, Dihedral group and Quaternion group of order 16 are computed. The obtained results are then applied to graph theory, more precisely to conjugate graph and conjugacy class graph. Some graph properties such as chromatic number, clique number, dominating number and independent number are found.   

Reciprocal degree distance and graph properties

2019 ◽  
Vol 258 ◽  
pp. 1-7
Author(s):  
Mingqiang An ◽  
Yinan Zhang ◽  
Kinkar Ch. Das ◽  
Liming Xiong
Keyword(s):  
Graph Properties ◽  
Degree Distance
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