scholarly journals Upper Bounds for Perfect Matchings in Pfaffian and Planar Graphs

10.37236/2845 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Afshin Behmaram ◽  
Shmuel Friedland
Keyword(s):  
Planar Graphs ◽  
Upper Bounds ◽  
Perfect Matchings ◽  
Pfaffian Graphs ◽  
Better Than ◽  
Fullerene Graphs

We give upper bounds on weighted perfect matchings in Pfaffian graphs. These upper bounds are better than Bregman's upper bounds on the number of perfect matchings. We show that some of our upper bounds are sharp for 3 and 4-regular Pfaffian graphs. We apply our results to fullerene graphs.

scholarly journals Some Bounds for the Kirchhoff Index of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yujun Yang
Keyword(s):  
Connected Graph ◽  
Planar Graphs ◽  
Independence Number ◽  
Clique Number ◽  
Upper Bounds ◽  
Electrical Network ◽  
Lower And Upper Bounds ◽  
Kirchhoff Index ◽  
Resistance Distance ◽  
Fullerene Graphs

The resistance distance between two vertices of a connected graphGis defined as the effective resistance between them in the corresponding electrical network constructed fromGby replacing each edge ofGwith a unit resistor. The Kirchhoff index ofGis the sum of resistance distances between all pairs of vertices. In this paper, general bounds for the Kirchhoff index are given via the independence number and the clique number, respectively. Moreover, lower and upper bounds for the Kirchhoff index of planar graphs and fullerene graphs are investigated.

Optimization Design of Electromagnetic Devices Using an Enhanced Salp Swarm Algorithm

2021 ◽  
Vol 35 (12) ◽  
pp. 1471-1476
Author(s):  
Houssem Bouchekara ◽  
Mostafa Smail ◽  
Mohamed Javaid ◽  
Sami Shamsah
Keyword(s):  
Optimization Design ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Design Problems ◽  
Salp Swarm Algorithm ◽  
Electromagnetic Devices ◽  
Swarm Algorithm ◽  
Better Than

An Enhanced version of the Salp Swarm Algorithm (SSA) referred to as (ESSA) is proposed in this paper for the optimization design of electromagnetic devices. The ESSA has the same structure as of the SSA with some modifications in order to enhance its performance for the optimization design of EMDs. In the ESSA, the leader salp does not move around the best position with a fraction of the distance between the lower and upper bounds as in the SAA; rather, a modified mechanism is used. The performance of the proposed algorithm is tested on the widely used Loney’s solenoid and TEAM Workshop Problem 22 design problems. The obtained results show that the proposed algorithm is much better than the initial one. Furthermore, a comparison with other well-known algorithms revealed that the proposed algorithm is very competitive for the optimization design of electromagnetic devices.

scholarly journals A Note on Domino Shuffling

10.37236/1056 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
É. Janvresse ◽  
T. de la Rue ◽  
Y. Velenik
Keyword(s):  
Large Class ◽  
Planar Graphs ◽  
Perfect Matchings ◽  
Sufficient Condition ◽  
Aztec Diamond

We present a variation of James Propp's generalized domino shuffling, which provides an efficient way to obtain perfect matchings of weighted Aztec diamonds. Our modification is specially tailored to deal with cases when some of the weights are zero. This allows us to tile efficiently a large class of planar graphs, by embedding them in a large enough Aztec diamond. We also give a sufficient condition on the size of the latter diamond for the algorithm to succeed.

scholarly journals The Cube Recurrence

10.37236/1826 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Gabriel D. Carroll ◽  
David Speyer
Keyword(s):  
Recurrence Relation ◽  
Planar Graphs ◽  
Perfect Matchings ◽  
Laurent Polynomials ◽  
Combinatorial Interpretation ◽  
Combinatorial Model

We construct a combinatorial model that is described by the cube recurrence, a quadratic recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in ${\Bbb Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky about the structure of these polynomials, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences, including the Somos-6 and Somos-7 sequences. We also indicate how the model might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs.

ON THE QUASI-STATIONARY DISTRIBUTION OF SIS MODELS

2016 ◽  
Vol 30 (4) ◽  
pp. 622-639 ◽  
Author(s):  
Gaofeng Da ◽  
Maochao Xu ◽  
Shouhuai Xu
Keyword(s):  
Stationary Distribution ◽  
Upper Bound ◽  
Hazard Rate ◽  
State Of The Art ◽  
Upper Bounds ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Novel Method ◽  
Better Than ◽  
Quasi Stationary Distribution

In this paper, we propose a novel method for constructing upper bounds of the quasi-stationary distribution of SIS processes. Using this method, we obtain an upper bound that is better than the state-of-the-art upper bound. Moreover, we prove that the fixed point map Φ [7] actually preserves the equilibrium reversed hazard rate order under a certain condition. This allows us to further improve the upper bound. Some numerical results are presented to illustrate the results.

New upper bounds on linear coloring of planar graphs

2011 ◽  
Vol 28 (6) ◽  
pp. 1187-1196 ◽  
Author(s):  
Bin Liu ◽  
Gui Zhen Liu
Keyword(s):  
Planar Graphs ◽  
Upper Bounds

ROUTING BALANCED COMMUNICATIONS ON HAMILTON DECOMPOSABLE NETWORKS

2004 ◽  
Vol 14 (03n04) ◽  
pp. 377-385 ◽  
Author(s):  
LADISLAV STACHO ◽  
JOZEF ŠIRÁŇ ◽  
SANMING ZHOU
Keyword(s):  
Wave Length ◽  
Upper Bounds ◽  
Ring Network ◽  
Special Case ◽  
Better Than

In [10] the authors proved upper bounds for the arc-congestion and wave-length number of any permutation demand on a bidirected ring. In this note, we give generalizations of their results in two directions. The first one is that instead of considering only permutation demands we consider any balanced demand, and the second one is that instead of the ring network we consider any Hamilton decomposable network. Thus, we obtain upper bounds (which are best possible in general) for the arc-congestion and wavelength number of any balanced demand on a Hamilton decomposable network. As a special case, we obtain upper bounds on arc- and edge-forwarding indices of Hamilton decomposable networks that are in many cases better than the known ones.

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