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Search: MSC category 05C50 ( Graphs and linear algebra (matrices, eigenvalues, etc.) )

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1. CMB 2014 (vol 57 pp. 520)

Guo, Guangquan; Wang, Guoping
 Maximizing the Index of Trees with Given Domination Number The index of a graph $G$ is the maximum eigenvalue of its adjacency matrix $A(G)$. In this paper we characterize the extremal tree with given domination number that attains the maximum index. Keywords:trees, spectral radius, index, domination numberCategory:05C50

2. CMB 2008 (vol 51 pp. 413)

Thé, L. Nguyen Van
 Big Ramsey Degrees and Divisibility in Classes of Ultrametric Spaces Given a countable set $S$ of positive reals, we study finite-dimensional Ramsey-theoretic properties of the countable ultrametric Urysohn space $\textbf{Q} _S$ with distances in $S$. Keywords:Ramsey theory, Urysohn metric spaces, ultrametric spacesCategories:05C50, 54E35

3. CMB 2002 (vol 45 pp. 321)

Brenken, Berndt
 $C^{\ast}$-Algebras of Infinite Graphs and Cuntz-Krieger Algebras The Cuntz-Krieger algebra $\mathcal{O}_B$ is defined for an arbitrary, possibly infinite and infinite valued, matrix $B$. A graph $C^{\ast}$-algebra $G^{\ast} (E)$ is introduced for an arbitrary directed graph $E$, and is shown to coincide with a previously defined graph algebra $C^{\ast} (E)$ if each source of $E$ emits only finitely many edges. Each graph algebra $G^{\ast} (E)$ is isomorphic to the Cuntz-Krieger algebra $\mathcal{O}_B$ where $B$ is the vertex matrix of~$E$. Categories:46LXX, 05C50