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Locating the extremal entries of the Fiedler vector for rose trees
Author(s) -
Gernandt Hannes
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900408
Subject(s) - rose (mathematics) , mathematics , star (game theory) , combinatorics , eigenvalues and eigenvectors , graph , path (computing) , path graph , mathematical analysis , computer science , physics , geometry , graph power , line graph , programming language , quantum mechanics
In this note we locate the extremal entries of the Fiedler vector for the class of rose trees, which consists of paths with a star graph attached to it. We derive directly from the eigenvector equation conditions to characterize in which cases the extremal values are located either at the end points of the path or on the pendant vertices of the star graph.