A graph is said to be (Δ, δ)-bidegreed if vertices all have one of two possible degrees: the maximum degree Δ or the minimum degree δ, with Δ, ≠ δ. We show that in the set of connected (Δ, 1)- bidegreed graphs, other than trees, with prescribed degree sequence, the graphs minimizing the adjacency matrix spectral radius cannot have vertices adjacent to Δ - 1 vertices of degree 1, that is, there are not any hanging trees. Further we consider the limit point for the spectral radius of (Δ, 1)-bidegreed graphs when degree Δ vertices are inserted in each edge between any two degree Δ vertices.

On the structure of bidegreed graphs with minimal spectral radius / Belardo, Francesco. - In: FILOMAT. - ISSN 0354-5180. - 28:1(2014), pp. 1-10. [10.2298/FIL1401001B]

On the structure of bidegreed graphs with minimal spectral radius

BELARDO, Francesco
2014

Abstract

A graph is said to be (Δ, δ)-bidegreed if vertices all have one of two possible degrees: the maximum degree Δ or the minimum degree δ, with Δ, ≠ δ. We show that in the set of connected (Δ, 1)- bidegreed graphs, other than trees, with prescribed degree sequence, the graphs minimizing the adjacency matrix spectral radius cannot have vertices adjacent to Δ - 1 vertices of degree 1, that is, there are not any hanging trees. Further we consider the limit point for the spectral radius of (Δ, 1)-bidegreed graphs when degree Δ vertices are inserted in each edge between any two degree Δ vertices.
2014
On the structure of bidegreed graphs with minimal spectral radius / Belardo, Francesco. - In: FILOMAT. - ISSN 0354-5180. - 28:1(2014), pp. 1-10. [10.2298/FIL1401001B]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/618959
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