Bibliographic Details
| Title: |
Algebraic connectivity in normed spaces. |
| Authors: |
Cruickshank, James1 (AUTHOR) james.cruickshank@universityofgalway.ie, Dewar, Sean2 (AUTHOR) sean.dewar@bristol.ac.uk, Kitson, Derek1,3 (AUTHOR) derek.kitson@mic.ul.ie |
| Source: |
Linear Algebra & its Applications. Jun2026, Vol. 739, p10-42. 33p. |
| Subjects: |
Graph theory, Geometric rigidity, Graph connectivity, Metric spaces, Isomorphism (Mathematics) |
| Abstract: |
The algebraic connectivity of a graph G in a finite dimensional real normed linear space X is a geometric counterpart to the Fiedler number of the graph and can be regarded as a measure of the rigidity of the graph in X. We analyse the behaviour of the algebraic connectivity of G in X with respect to graph decomposition, vertex deletion and isometric isomorphism, and provide a general bound expressed in terms of the geometry of X and the Fiedler number of the graph. Particular focus is given to the space ℓ ∞ d where we present explicit formulae and calculations as well as upper and lower bounds. As a key tool, we show that the monochrome subgraphs of a complete framework in ℓ ∞ d are odd-hole-free. Connections to redundant rigidity are also presented. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
