scholarly journals Graphs with Obstacle Number Greater than One

2017 ◽  
Vol 21 (6) ◽  
pp. 1107-1119
Author(s):  
Leah Wrenn Berman ◽  
Glenn G. Chappell ◽  
Jill R. Faudree ◽  
John Gimbel ◽  
Chris Hartman ◽  
...  
Keyword(s):  
Obstacle Number

scholarly journals On Obstacle Numbers

10.37236/4373 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Vida Dujmović ◽  
Pat Morin
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Obstacle Number

The obstacle number is a new graph parameter introduced by Alpert, Koch, and Laison (2010). Mukkamala et al. (2012) show that there exist graphs with $n$ vertices having obstacle number in $\Omega(n/\log n)$. In this note, we up this lower bound to $\Omega(n/(\log\log n)^2)$. Our proof makes use of an upper bound of Mukkamala et al. on the number of graphs having obstacle number at most $h$ in such a way that any subsequent improvements to their upper bound will improve our lower bound.

scholarly journals Lower Bounds on the Obstacle Number of Graphs

10.37236/2380 ◽  
2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Padmini Mukkamala ◽  
János Pach ◽  
Dömötör Pálvölgyi
Keyword(s):  
Lower Bounds ◽  
Minimum Number ◽  
Obstacle Number ◽  
Set Of Points

Given a graph $G$, an obstacle representation of $G$ is a set of points in the plane representing the vertices of $G$, together with a set of connected obstacles such that two vertices of $G$ are joined by an edge if and only if the corresponding points can be connected by a segment which avoids all obstacles. The obstacle number of $G$ is the minimum number of obstacles in an obstacle representation of $G$. It is shown that there are graphs on $n$ vertices with obstacle number at least $\Omega({n}/{\log n})$.

scholarly journals Transmission probability through zigzag monolayer phosphorene superlattice

2021 ◽  
Author(s):  
Atena boroughani ◽  
Edris Faizabadi ◽  
Hamed Hedayati
Keyword(s):  
Transfer Matrix Method ◽  
Essential Role ◽  
Structural Parameters ◽  
Transmission Probability ◽  
Charge Carriers ◽  
The Other ◽  
The Novel ◽  
Two Dimensional ◽  
Superlattice Structures ◽  
Obstacle Number

Abstract The transportation of charge carriers for monolayer phosphorene superlattice has been investigated utilizing a transfer matrix method. Also, the efficacy of structural parameters has been studied on the transmission of charge carriers for the system. Our findings demonstrated that the barrier number at the superlattice structures performs an essential role in the transportation probability, that can be utilized in the design of nanoelectronic sets. Further, it can be comprehended that the transmission probability of one for the normal incident has occurred in twenty obstacles. On the other hand, the transmission probability of close to one has occurred in lower landing energies by increasing the obstacle number. As well, it has been understood the transmission probability of close to one by enhancing the barrier number can happen in barriers with a smaller width. According to the results, phosphorene can be used in the novel advances of two dimensional semiconductor devices in electronic applications.

scholarly journals On the Structure of Graphs with Low Obstacle Number

2011 ◽  
Vol 27 (3) ◽  
pp. 465-473 ◽  
Author(s):  
János Pach ◽  
Deniz Sarıöz
Keyword(s):  
Obstacle Number

scholarly journals Transmission probability through zigzag monolayer phosphorene superlattice

2021 ◽  
Author(s):  
Atena boroughani ◽  
Edris Faizabadi ◽  
Hamed Hedayati
Keyword(s):  
Transfer Matrix Method ◽  
Essential Role ◽  
Structural Parameters ◽  
Transmission Probability ◽  
Charge Carriers ◽  
The Other ◽  
The Novel ◽  
Two Dimensional ◽  
Superlattice Structures ◽  
Obstacle Number

Abstract The transportation of charge carriers for monolayer phosphorene superlattice has been investigated utilizing a transfer matrix method. Also, the efficacy of structural parameters has been studied on the transmission of charge carriers for the system. Our findings demonstrated that the barrier number at the superlattice structures performs an essential role in the transportation probability, that can be utilized in the design of nanoelectronic sets. Further, it can be comprehended that the transmission probability of one for the normal incident has occurred in twenty obstacles. On the other hand, the transmission probability of close to one has occurred in lower landing energies by increasing the obstacle number. As well, it has been understood the transmission probability of close to one by enhancing the barrier number can happen in barriers with a smaller width. According to the results, phosphorene can be used in the novel advances of two dimensional semiconductor devices in electronic applications.

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