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On approximating shortest paths in weighted triangular tessellations
(Springer, 2022)
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We study the quality of weighted shortest paths when a continuous 2-dimensional space is discretized by a weighted triangular tessellation. In order to evaluate how well the tessellation approximates the 2-dimensional ...
Continuous mean distance of a weighted graph
(2022)
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We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance can be defined as the arithmetic mean of the distances between all pairs of vertices. This parameter ...
Algorithmic geometry with infinite time computation
(2021)
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Spanning ratio of shortest paths in weighted square tessellations
(2022)
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Continuous 2-dimensional space is often discretized by considering a grid of weighted square cells. In this work we study how well a weighted tessellation approximates the space, with respect to shortest paths. In particular, ...
Shortest paths in portalgons
(Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023)
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Any surface that is intrinsically polyhedral can be represented by a collection of simple polygons (fragments), glued along pairs of equally long oriented edges, where each fragment is endowed with the geodesic metric ...
Some results on the laplacian spectra of Token graphs
(Springer, 2021)
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We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph Fk(G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent ...
Graphs attaining the upper bound on the isolation number
(Universidad de Cádiz, 2023)
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A set D of vertices of a graph is isolating if the set of vertices not belonging to D or not having a neighbour in D is independent. The isolation number of a graph G, denoted by ¿(G), is the minimum cardinality of an ...
Shortest coordinated motion for square robots
(Springer, 2023)
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We study the problem of determining minimum-length coordinated motions for two axis-aligned square robots translating in an obstacle-free plane: Given feasible start and goal configurations, find a continuous motion for ...