منابع مشابه
Coverings, heat kernels and spanning trees
We consider a graph G and a covering G̃ of G and we study the relations of their eigenvalues and heat kernels. We evaluate the heat kernel for an infinite k-regular tree and we examine the heat kernels for general k-regular graphs. In particular, we show that a k-regular graph on n vertices has at most (1 + o(1)) 2 log n kn log k ( (k − 1)k−1 (k2 − 2k)k/2−1 )n spanning trees, which is best possi...
متن کاملCoverings, Heat Kernels and Spanning Trees
We consider a graph G and a covering G̃ of G and we study the relations of their eigenvalues and heat kernels. We evaluate the heat kernel for an infinite k-regular tree and we examine the heat kernels for general k-regular graphs. In particular, we show that a k-regular graph on n vertices has at most (1 + o(1)) 2 log n kn log k (k − 1)k−1 (k2 − 2k)k/2−1 n spanning trees, which is best possible...
متن کاملCoverings, Laplacians, and Heat Kernels of Directed Graphs
Combinatorial covers of graphs were defined by Chung and Yau. Their main feature is that the spectra of the Combinatorial Laplacian of the base and the total space are related. We extend their definition to directed graphs. As an application, we compute the spectrum of the Combinatorial Laplacian of the homesick random walk RWμ on the line. Using this calculation, we show that the heat kernel o...
متن کاملHeat Kernels of Metric Trees and Applications
We consider the heat semigroup generated by the Laplace operator on metric trees. Among our results we show how the behavior of the associated heat kernel depends on the geometry of the tree. As applications we establish new eigenvalue estimates for Schrödinger operators on metric trees.
متن کاملNetworks and Spanning Trees
In 1857 Arthur Cayley (1821–1895) published a paper [9] that introduces the term “tree” to describe the logical branching that occurs when iterating the fundamental process of (partial) differentiation. When discussing the composition of four symbols that involve derivatives, Cayley writes “But without a more convenient notation, it would be difficult to find [their] corresponding expressions ....
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1998
ISSN: 1077-8926
DOI: 10.37236/1444