Let LG be the Laplacian matrix of a graph G with n vertices, and let b be a binary vector of length n. The pair (LG, b) is said to be controllable (and we also say that G is Laplacian controllable for b) if LG has no eigenvector orthogonal to b. In this paper we study the Laplacian controllability of joins, Cartesian products, tensor products and strong products of two graphs. Besides some theoretical results, we give an iterative construction of infinite families of controllable pairs (LG, b).
Laplacian Controllability for Graphs Obtained by Some Standard Products / Brunetti, M; Andelic, M; Stanic, Z. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - 36:5(2020), pp. 1593-1602. [10.1007/s00373-020-02212-6]
Laplacian Controllability for Graphs Obtained by Some Standard Products
Brunetti M;
2020
Abstract
Let LG be the Laplacian matrix of a graph G with n vertices, and let b be a binary vector of length n. The pair (LG, b) is said to be controllable (and we also say that G is Laplacian controllable for b) if LG has no eigenvector orthogonal to b. In this paper we study the Laplacian controllability of joins, Cartesian products, tensor products and strong products of two graphs. Besides some theoretical results, we give an iterative construction of infinite families of controllable pairs (LG, b).| File | Dimensione | Formato | |
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