scholarly journals A Graph Pebbling Algorithm on Weighted Graphs

2010 ◽  
Vol 14 (2) ◽  
pp. 221-244 ◽  
Author(s):  
Nandor Sieben
Keyword(s):  
Weighted Graphs ◽  
Graph Pebbling

scholarly journals The $t$-Pebbling Number is Eventually Linear in $t$

10.37236/640 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Michael Hoffmann ◽  
Jiří Matoušek ◽  
Yoshio Okamoto ◽  
Philipp Zumstein
Keyword(s):  
Initial Distribution ◽  
Adjacent Vertex ◽  
Weighted Graphs ◽  
Graph Pebbling ◽  
Pebbling Number ◽  
Integer Weight

In graph pebbling games, one considers a distribution of pebbles on the vertices of a graph, and a pebbling move consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The $t$-pebbling number $\pi_t(G)$ of a graph $G$ is the smallest $m$ such that for every initial distribution of $m$ pebbles on $V(G)$ and every target vertex $x$ there exists a sequence of pebbling moves leading to a distibution with at least $t$ pebbles at $x$. Answering a question of Sieben, we show that for every graph $G$, $\pi_t(G)$ is eventually linear in $t$; that is, there are numbers $a,b,t_0$ such that $\pi_t(G)=at+b$ for all $t\ge t_0$. Our result is also valid for weighted graphs, where every edge $e=\{u,v\}$ has some integer weight $\omega(e)\ge 2$, and a pebbling move from $u$ to $v$ removes $\omega(e)$ pebbles at $u$ and adds one pebble to $v$.

Heat Kernel Estimates on Weighted Graphs

2000 ◽  
Vol 32 (4) ◽  
pp. 477-483 ◽  
Author(s):  
Bernd Metzger ◽  
Peter Stollmann
Keyword(s):  
Heat Kernel ◽  
Weighted Graphs ◽  
Kernel Estimates ◽  
Heat Kernel Estimates

scholarly journals Path ideals of weighted graphs

2015 ◽  
Vol 219 (9) ◽  
pp. 3889-3912 ◽  
Author(s):  
Bethany Kubik ◽  
Sean Sather-Wagstaff
Keyword(s):  
Weighted Graphs

scholarly journals Spread of Epidemic Disease on Edge-Weighted Graphs from a Database: A Case Study of COVID-19

2021 ◽  
Vol 18 (9) ◽  
pp. 4432
Author(s):  
Ronald Manríquez ◽  
Camilo Guerrero-Nancuante ◽  
Felipe Martínez ◽  
Carla Taramasco
Keyword(s):  
Public Health ◽  
Infectious Diseases ◽  
Preventive Measures ◽  
Weighted Graph ◽  
Real Data ◽  
Sir Model ◽  
Weighted Graphs ◽  
Epidemic Disease ◽  
The Real

The understanding of infectious diseases is a priority in the field of public health. This has generated the inclusion of several disciplines and tools that allow for analyzing the dissemination of infectious diseases. The aim of this manuscript is to model the spreading of a disease in a population that is registered in a database. From this database, we obtain an edge-weighted graph. The spreading was modeled with the classic SIR model. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics. Moreover, a deterministic approximation is provided. With database COVID-19 from a city in Chile, we analyzed our model with relationship variables between people. We obtained a graph with 3866 vertices and 6,841,470 edges. We fitted the curve of the real data and we have done some simulations on the obtained graph. Our model is adjusted to the spread of the disease. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics, in this case with real data of COVID-19. This valuable information allows us to also include/understand the networks of dissemination of epidemics diseases as well as the implementation of preventive measures of public health. These findings are important in COVID-19’s pandemic context.

Classification of Linear Weighted Graphs up to Blowing-Up and Blowing-Down

2008 ◽  
Vol 60 (1) ◽  
pp. 64-87 ◽  
Author(s):  
Daniel Daigle
Keyword(s):  
Algebraic Surfaces ◽  
Weighted Graphs ◽  
Blowing Up

AbstractWe classify linear weighted graphs up to the blowing-up and blowing-down operations which are relevant for the study of algebraic surfaces.

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