On the First Eigenvalue of the Combinatorial Laplacian for a Graph

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概要

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• The eigenvalues of the combinatorial Laplacian of graphs with boundaries and infinite graphs without boundary are studied. For a graph with boundary G =(V ∪∂V,E ∪∂E ), a sharp lower bound of the first eigenvalue λ1(G ) is given provided G satisfies a general condition, the so called non-separation property. For an infinite graph G without boundary, the bottom of the spectrum, i.e., the infimum of the spectrum of the combinatorial Laplacian of G, denoted λ0(G ), is estimated as λ0(G ) ≤ ¼ μ(G )2exp(μ(G )),where μ(G ) is the exponential growth of G. As a corollary, if G is subexponential, λ0(G )=0. On the contrary,λ0(G ) >0 is shown for a simply connected infinite graph G with degree ≥4 at each vertex.

• 東北大学の論文

著者

• Urakawa Hajime

  Graduate School Of Information Sciences Tohoku University

• OHNO Yoshiki

  Faculty of Engineering, Tohoku University

• Ohno Yoshiki

  Faculty Of Engineering Tohoku University

関連論文

• On the First Eigenvalue of the Combinatorial Laplacian for a Graph

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