Cleavages of graphs: the spectral radius |
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Authors: | José A de la Peña |
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Institution: | 1. Instituto de Matemáticas, UNAM. Cd. Universitaria , México City, 04510 D.F.jap@matem.unam.mx |
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Abstract: | A cleavage of a finite graph G is a morphism f : H → G of graphs such that if P is the m × n characteristic matrix defined as P ik = 1 if i ∈ f ?1(k), otherwise = 0, then A(H)P ≤ PA(G), where A(G) and A(H) are the adjacency matrices of G and H, respectively. This concept generalizes induced subgraphs, quotients of graphs, Galois covers, path-tree graphs and others. We show that for spectral radii we have the inequality ρ(H) ≤ ρ(G). Equality holds only in case f : H → G is an equivariant quotient and H has isoperimetric constant i(H) = 0. |
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Keywords: | Cleavage quivers Galois cover finite graph equivariant quotient spectral radius |
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