We consider two classes of graphs: (i) trees of order n and diameter d =n - 3 and (ii) unicyclic graphs of order n and girth g = n - 2. Assuming that each graph within these classes has two vertices of degree 3 at distance k, we order by the index (i.e. spectral radius) the graphs from (i) for any fixed k (1 ≤ k ≤ d - 2), and the graphs from (ii) independently of k. © 2006 Elsevier Inc. All rights reserved.
Some notes on graphs whose index is close to 2
BELARDO, FRANCESCO;LI MARZI, Enzo;
2007-01-01
Abstract
We consider two classes of graphs: (i) trees of order n and diameter d =n - 3 and (ii) unicyclic graphs of order n and girth g = n - 2. Assuming that each graph within these classes has two vertices of degree 3 at distance k, we order by the index (i.e. spectral radius) the graphs from (i) for any fixed k (1 ≤ k ≤ d - 2), and the graphs from (ii) independently of k. © 2006 Elsevier Inc. All rights reserved.File in questo prodotto:
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