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Your search keyword '"Napolitano, V"' showing total 15 results
Start Over Author "Napolitano, V" Publisher elsevier b.v.
15 results on '"Napolitano, V"'

7. On projective spaces with.

Author

Durante, N., Napolitano, V., and Olanda, D.

Subjects
HYPERBOLIC spaces, NON-Euclidean geometry, FOUNDATIONS of geometry, PARALLELS (Geometry)
Abstract

Abstract: A characterization of , , in terms of planar spaces is given. [Copyright &y& Elsevier]

Published
2006
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15. Invariant adjacency matrices of configuration graphs

Author

Abreu, M., Funk, M.J., Labbate, D., and Napolitano, V.

Subjects
*INVARIANTS (Mathematics), *MATRICES (Mathematics), *GRAPH theory, *ISOMORPHISM (Mathematics), *PETERSEN graphs, *MATHEMATICAL mappings, *MATHEMATICAL symmetry
Abstract

Abstract: Some graphs Γ have the following property : the configuration graph (i.e. the non–collinearity graph) of the neighbourhood geometry of Γis isomorphic to Γ. For instance, the ubiquitous Petersen graph satisfies . The purpose of this paper is to reveal repercussions of property on adjacency matrices A for Γ. This will be achieved in terms of invariance under (powers of) the following mapping Θ: denote by I and J the identity matrix and the all one matrix, respectively, both of order n = k 2+1, and define Θ(A) := (k−1)I + J−A 2. If k =3 and A is an adjacency matrix for the Petersen graph, it is well known that Θ(A)= A. In 1960, Hoffman and Singleton showed that for arbitrary k the matrix equation Θ(A)= A has only very few solutions, namely for k =2,3,7 and possibly for k =57. We prove that the property implies the existence of an integer m ⩾1 such that Θ m (A)= A. We determine a standard form for such matrices which is invariant under the action of Θ. In particular, we characterize all solutions, on A, to Θ m (A)= A for k =3 and k =4, where A is an adjacency matrix of some k–regular graph, solving a conjecture posed by the authors. [Copyright &y& Elsevier]

Published
2012
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