On the structure of bidegreed graphs with minimal spectral radius | Zendy

Francesco Belardo | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

On the structure of bidegreed graphs with minimal spectral radius

Author(s) -

Francesco Belardo

Publication year - 2014

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1401001b

Subject(s) - mathematics , combinatorics , spectral radius , adjacency matrix , degree (music) , frequency partition of a graph , chordal graph , metric dimension , adjacency list , discrete mathematics , graph , 1 planar graph , eigenvalues and eigenvectors , graph power , line graph , physics , quantum mechanics , acoustics

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

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research