
Constructing minimally 3connected graphs
A 3connected graph is minimally 3connected if removal of any edge dest...
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Graphical Construction of Spatial Gibbs Random Graphs
We present a Spatial Gibbs Random Graphs Model that incorporates the int...
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Numerical Integration on Graphs: where to sample and how to weigh
Let G=(V,E,w) be a finite, connected graph with weighted edges. We are i...
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Restless reachability problems in temporal graphs
We study a family of reachability problems under waitingtime restrictio...
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Total 2domination of proper interval graphs
A set of vertices W of a graph G is a total kdominating set when every ...
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Eulerian edge refinements, geodesics, billiards and sphere coloring
A finite simple graph is called a 2graph if all of its unit spheres S(x...
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Connected Components in Undirected Set–Based Graphs. Applications in Object–Oriented Model Manipulation
This work introduces a novel algorithm for finding the connected compone...
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Dynamics of epidemic spreading on connected graphs
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDEODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by heat equations on the edges supplemented with Robin like boundary conditions at the vertices modeling exchanges between incident edges and the associated vertex. We describe the main properties of the system, and also derive the final total population of infected individuals. We present a semiimplicit in time numerical scheme based on finite differences in space which preserves the main properties of the continuous model such as the uniqueness and positivity of solutions and the conservation of the total population. We also illustrate our results with a selection of numerical simulations for a selection of connected graphs.
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