On the Colin de Verdière graph number and penny graphs

DOI10.1016/j.laa.2024.10.026MaRDI QIDQ6650590

Abdo Y. Alfakih

Publication date: 9 December 2024

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Euclidean distance matricespenny graphsColin de Verdière graph number

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48) Graph representations (geometric and intersection representations, etc.) (05C62)

Cites Work

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• Properties of Euclidean and non-Euclidean distance matrices
• The Colin de Verdière number and sphere representations of a graph
• The logic engine and the realization problem for nearest neighbor graphs
• Sur un nouvel invariant des graphes et un critère de planarité. (On a new graph invariant and a planarity criterion)
• On the invariance of Colin de Verdière's graph parameter under clique sums
• Circum-Euclidean distance matrices and faces
• Discussion of a set of points in terms of their mutual distances.
• Remarks to Maurice Fréchet's article ``Sur la définition axiomatique d'une classe d'espaces vectoriels distanciés applicables vectoriellement sur l'espace de Hilbert.
• Efficient Planarity Testing
• Euclidean Distance Matrices and Their Applications in Rigidity Theory
• Edge Bounds and Degeneracy of Triangle-Free Penny Graphs and Squaregraphs
• k-Degenerate Graphs

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