منابع مشابه
The generalized spectral radius and extremal norms
The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm always exists. This approach lends itself easily to the analysis of further properties of the generali...
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© Annales de l’institut Fourier, 1963, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier...
متن کاملExtremal Problems for the p-Spectral Radius of Graphs
The p-spectral radius of a graph G of order n is defined for any real number p > 1 as λ (G) = max 2 ∑ {i,j}∈E(G) xixj : x1, . . . , xn ∈ R and |x1| + · · ·+ |xn| = 1 . The most remarkable feature of λ(p) is that it seamlessly joins several other graph parameters, e.g., λ(1) is the Lagrangian, λ(2) is the spectral radius and λ(∞)/2 is the number of edges. This paper presents solutions to so...
متن کاملExtremal unicyclic graphs with minimal distance spectral radius
The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m 6= 3). In this paper, we determine the extremal unicyclic graph which has minimal distance spectral radius in U (n,m) \ Cn.
متن کاملEccentric Connectivity Index: Extremal Graphs and Values
Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1968
ISSN: 0386-5991
DOI: 10.2996/kmj/1138845748