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Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes

Gyula Y. Katona, Morteza Faghani, Ali Reza Ashrafi (2014)

Discussiones Mathematicae Graph Theory

The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.

Cohomologie de Hochschild des graphes de Kontsevich

Didier Arnal, Mohsen Masmoudi (2002)

Bulletin de la Société Mathématique de France

Nous calculons la cohomologie de Hochschild directement sur les graphes de Kontsevich. Celle-ci est localisée sur les graphes totalement antisymétriques ayant autant de pieds que de pattes. La considération de cette cohomologie permet de réinterpréter l’équation de formalité pour l’espace ℝ d .

Commuting contractive families

Luka Milićević (2015)

Fundamenta Mathematicae

A family f₁,..., fₙ of operators on a complete metric space X is called contractive if there exists a positive λ < 1 such that for any x,y in X we have d ( f i ( x ) , f i ( y ) ) ≤ λ d ( x , y ) for some i. Austin conjectured that any commuting contractive family of operators has a common fixed point, and he proved this for the case of two operators. We show that Austin’s conjecture is true for three operators, provided that λ is sufficiently small.

Composition and structure of social networks

Ove Frank (1997)

Mathématiques et Sciences Humaines

Social networks representing one or more relationships between individuals and one or more categorical characteristics of the individuals exhibit both structure and composition. Probabilistic models of such networks can be used for analyzing the interrelations between structural and compositional variables, for instance in order to find how structure can be explained by composition or how structure explains composition. Different models are discussed and different statistical methods are employed...

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