On the z-counting polynomial for edge-weighted graphs

1992 ◽  
Vol 9 (4) ◽  
pp. 381-387 ◽  
Author(s):  
Sonja Nikolić ◽  
Dejan Plavšić ◽  
Nenad Trinajstić
Keyword(s):  
Weighted Graphs ◽  
Counting Polynomial

scholarly journals Orbit Polynomial of Graphs versus Polynomial with Integer Coefficients

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 710
Author(s):  
Modjtaba Ghorbani ◽  
Maryam Jalali-Rad ◽  
Matthias Dehmer
Keyword(s):  
Integer Coefficients ◽  
Integer Polynomial ◽  
Counting Polynomial

Suppose ai indicates the number of orbits of size i in graph G. A new counting polynomial, namely an orbit polynomial, is defined as OG(x) = ∑i aixi. Its modified version is obtained by subtracting the orbit polynomial from 1. In the present paper, we studied the conditions under which an integer polynomial can arise as an orbit polynomial of a graph. Additionally, we surveyed graphs with a small number of orbits and characterized several classes of graphs with respect to their orbit polynomials.

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.

scholarly journals Counting polynomial subset sums

2018 ◽  
Vol 47 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Jiyou Li ◽  
Daqing Wan
Keyword(s):  
Subset Sums ◽  
Counting Polynomial
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