منابع مشابه
Cogrowth of Regular Graphs
Let & be a ¿-regular graph and T the covering tree of S. We define a cogrowth constant of & in T and express it in terms of the first eigenvalue of the Laplacian on S . As a corollary, we show that the cogrowth constant is as large as possible if and only if the first eigenvalue of the Laplacian on 9 is zero. Grigorchuk's criterion for amenability of finitely generated groups follows. In this n...
متن کاملNon-backtracking Random Walks and Cogrowth of Graphs
Let X be a locally finite, connected graph without vertices of degree 1. Non-backtracking random walk moves at each step with equal probability to one of the “forward” neighbours of the actual state, i.e., it does not go back along the preceding edge to the preceding state. This is not a Markov chain, but can be turned into a Markov chain whose state space is the set of oriented edges of X . Th...
متن کاملD-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs
The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...
متن کاملOPTIMAL ANALYSIS OF NON-REGULAR GRAPHS USING THE RESULTS OF REGULAR MODELS VIA AN ITERATIVE METHOD
In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the ...
متن کاملOPTIMAL ANALYSIS OF NON-REGULAR GRAPHS USING THE RESULTS OF REGULAR MODELS VIA AN ITERATIVE METHOD
In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of th...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1992-1120509-0