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1. CMB Online first
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 number Category:05C50 |
2. CMB 2008 (vol 51 pp. 413)
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 spaces Categories:05C50, 54E35 |
3. CMB 2002 (vol 45 pp. 321)
$C^{\ast}$-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 |