This work compares ball-and weighted graphs and gives a complete comparison in the one-dimensional case, and shows that the minimal dimension for ball graphs can at most be one larger than the minimal dimension for weighted graphs (weighted dimension), but also that the weighted dimension can exceed the ball dimension by an arbitrary amount.
Topological graph theory studies graphs in relation to the surfaces on which they can be drawn. This review presents the main classical ideas of the field in a clear and connected framework. It begins with graph embeddings, Euler’s formula, and the basic principles of planar graphs. It then discusses important classica...
Ghadeer Khudhair Obayes, Karrar Khudhair Obayes· Asian journal of mathematics...· 0 citations
A metric graph is a metric space obtained from a finite collection of intervals whose endpoints are identified in groups. It can also be seen as a finite, edge-weighted graph where the continuum of points along the interior of each edge is taken into consideration, and each edge is locally isometric to an interval whos...
Hee-Kap Ahn, Sergio Cabello, O. Cheong et al.· 0 citations
The findings illustrate that geometric insights grounded in hyperbolic geometry can offer powerful tools for understanding, embedding, and visualizing complex graph structures.
†. SalouaNaama, Kave Salamatian, M. Crovella· 0 citations
The existence and construction of distance magic labelings for certain families of complete bipartite graphs are investigated to contribute to the understanding of how arithmetic structure and partition properties influence the existence of distance magic labelings.
Kaveesha V. Senarathna, Sujeeva Wijesiri, S. Almeida· Symmetry· 0 citations
A graphical design is a subset of vertices of a graph, along with a weight for each chosen vertex, that can perfectly average chosen subspaces of functions on the graph. A design is uniformly weighted if all the weights are equal, and several well-known combinatorial objects such as orthogonal arrays, combinatorial blo...
Zawad Chowdhury, Rekha R. Thomas· 0 citations
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