On colored digraphs with exactly one nonsingular cycle | Zendy

Debajit Kalita | Zendy

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On colored digraphs with exactly one nonsingular cycle

Author(s) -

Debajit Kalita

Publication year - 2012

Publication title -

electronic journal of linear algebra

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.447

H-Index - 31

eISSN - 1537-9582

pISSN - 1081-3810

DOI - 10.13001/1081-3810.1529

Subject(s) - mathematics , combinatorics , algebraic connectivity , digraph , invertible matrix , eigenvalues and eigenvectors , algebraic number , colored , graph , discrete mathematics , laplacian matrix , laplace operator , pure mathematics , mathematical analysis , materials science , composite material , physics , quantum mechanics

The class of connected 3-colored digraphs containing exactly one nonsingular cycle is considered in this article. The main objective is to study the smallest Laplacian eigenvalue and the corresponding eigenvectors of such graphs. It is shown that the smallest Laplacian eigenvalue of such a graph can be realized as the algebraic connectivity (second smallest Laplacian eigenvalue) of a suitable undirected graph. The nonsingular unicyclic 3-colored digraph on n vertices, which minimize the smallest Laplacian eigenvalue over all such graphs is determined in this article.

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