Article
The spread of unicyclic graphs with given size of maximum matchings
Journal of Mathematical Chemistry (Impact Factor: 1.23). 01/2007; 42(4):775788. DOI: 10.1007/s1091000691416

Article: P01518  Quality of life and associated factors among chronic mental illness patients in Kaohsiung
European Psychiatry  EUR PSYCHIAT. 01/2011; 26:522522.  [Show abstract] [Hide abstract]
ABSTRACT: The inertia of a graph is an integer triple specifying the number of negative, zero, and positive eigenvalues of the adjacency matrix of the graph. A unicyclic graph is a simple connected graph with an equal number of vertices and edges. This paper characterizes the inertia of a unicyclic graph in terms of maximum matchings and gives a lineartime algorithm for computing it. Chemists are interested in whether the molecular graph of an unsaturated hydrocarbon is (properly) closedshell, having exactly half of its eigenvalues greater than zero, because this designates a stable electron configuration. The inertia determines whether a graph is closedshell, and hence the reported result gives a lineartime algorithm for determining this for unicyclic graphs.Linear Algebra and its Applications 01/2008; 429(4):849858. · 0.97 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the secondsmallest eigenvalue of the Laplacian matrix of the graph. Bao, Tan and Fan [Y.H. Bao, Y.Y. Tan,Y.Z. Fan, The Laplacian spread of unicyclic graphs, Appl. Math. Lett. 22 (2009) 1011–1015.] characterize the unique unicyclic graph with maximum Laplacian spread among all connected unicyclic graphs of fixed order. In this paper, we characterize the unique quasitree graph with maximum Laplacian spread among all quasitree graphs in the set Q(n,d) with 1⩽d⩽n42.Linear Algebra and its Applications 01/2011; 435(1):6066. · 0.97 Impact Factor
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